{"cells":[{"cell_type":"markdown","metadata":{"id":"4HLDufNbEyRb"},"source":["# Tutorial: Data as Objects and Tidy Data\n","\n","## Goals:\n","* Learn about Tidy Data, long data, and wide data\n","* Learn how to interact with model objects in R, including extracting coefficients"]},{"cell_type":"markdown","metadata":{"id":"riXmfzuPEyRc"},"source":["---\n","# Tidy Data"]},{"cell_type":"markdown","metadata":{"id":"GygYOYht0ZAK"},"source":["When you are working with data frames, it is best practice to keep your data **tidy**. **Tidy data** is a very specific term in which the following are true:\n","\n","* Columns are variables\n","* Rows are individual observations\n","* Observation for each variable is stored in the corresponding cell\n","\n","There are two versions of the tidy data format - long and wide. To illustrate the difference, imagine a repeated measures dataset, where you gather four observations for each subject at four different time points. In the **long data** format, each row represents an **observation** at a specific timepoint for a specific subject. Each subject has multiple rows of observations. The columns will be *subject*, *timepoint*, and *observation*. For example:"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":475},"executionInfo":{"elapsed":170,"status":"ok","timestamp":1706697252656,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"6P41tAP50ZAK","outputId":"492d1c7b-2cd5-47f0-b7d1-68c6062c3723"},"outputs":[{"output_type":"display_data","data":{"text/html":["\n","\n","\n","\t\n","\t\n","\n","\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\n","
A data.frame: 12 × 3
subjecttimepointobservation
<int><int><dbl>
11-1.09
12 0.10
13 0.84
14 1.09
21-0.81
22-0.13
23 0.76
24-0.44
31 2.09
32-1.62
33 0.95
34-0.09
\n"],"text/markdown":"\nA data.frame: 12 × 3\n\n| subject <int> | timepoint <int> | observation <dbl> |\n|---|---|---|\n| 1 | 1 | -1.09 |\n| 1 | 2 | 0.10 |\n| 1 | 3 | 0.84 |\n| 1 | 4 | 1.09 |\n| 2 | 1 | -0.81 |\n| 2 | 2 | -0.13 |\n| 2 | 3 | 0.76 |\n| 2 | 4 | -0.44 |\n| 3 | 1 | 2.09 |\n| 3 | 2 | -1.62 |\n| 3 | 3 | 0.95 |\n| 3 | 4 | -0.09 |\n\n","text/latex":"A data.frame: 12 × 3\n\\begin{tabular}{lll}\n subject & timepoint & observation\\\\\n & & \\\\\n\\hline\n\t 1 & 1 & -1.09\\\\\n\t 1 & 2 & 0.10\\\\\n\t 1 & 3 & 0.84\\\\\n\t 1 & 4 & 1.09\\\\\n\t 2 & 1 & -0.81\\\\\n\t 2 & 2 & -0.13\\\\\n\t 2 & 3 & 0.76\\\\\n\t 2 & 4 & -0.44\\\\\n\t 3 & 1 & 2.09\\\\\n\t 3 & 2 & -1.62\\\\\n\t 3 & 3 & 0.95\\\\\n\t 3 & 4 & -0.09\\\\\n\\end{tabular}\n","text/plain":[" subject timepoint observation\n","1 1 1 -1.09 \n","2 1 2 0.10 \n","3 1 3 0.84 \n","4 1 4 1.09 \n","5 2 1 -0.81 \n","6 2 2 -0.13 \n","7 2 3 0.76 \n","8 2 4 -0.44 \n","9 3 1 2.09 \n","10 3 2 -1.62 \n","11 3 3 0.95 \n","12 3 4 -0.09 "]},"metadata":{}}],"source":["long_data <- data.frame(subject = rep(1:3, each=4), # rep repeats a vector n times\n"," timepoint = rep(1:4, times=3), # same as previous\n"," observation = round(rnorm(12), 2)) #rnorm simulates a normal distribution\n","long_data # print out long data table"]},{"cell_type":"markdown","metadata":{"id":"gfjAUDkx0ZAL"},"source":["Alternatively, the data can be organized in a **wide format**, in which each row is a single **subject**, the four different timepoints are represented as different columns, and the observation for each timepoint is stored at a cell within that column. Like this (don't worry about the code for now, it is explained in the next tutorial):"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":192},"executionInfo":{"elapsed":162,"status":"ok","timestamp":1706697254525,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"f0gKFGvd0ZAL","outputId":"c5c7d7a3-b27a-4efb-951b-2eaec0b3d04e"},"outputs":[{"output_type":"display_data","data":{"text/html":["\n","\n","\n","\t\n","\t\n","\n","\n","\t\n","\t\n","\t\n","\n","
A data.frame: 3 × 5
subjecttime1time2time3time4
<int><dbl><dbl><dbl><dbl>
1-1.09 0.100.84 1.09
2-0.81-0.130.76-0.44
3 2.09-1.620.95-0.09
\n"],"text/markdown":"\nA data.frame: 3 × 5\n\n| subject <int> | time1 <dbl> | time2 <dbl> | time3 <dbl> | time4 <dbl> |\n|---|---|---|---|---|\n| 1 | -1.09 | 0.10 | 0.84 | 1.09 |\n| 2 | -0.81 | -0.13 | 0.76 | -0.44 |\n| 3 | 2.09 | -1.62 | 0.95 | -0.09 |\n\n","text/latex":"A data.frame: 3 × 5\n\\begin{tabular}{lllll}\n subject & time1 & time2 & time3 & time4\\\\\n & & & & \\\\\n\\hline\n\t 1 & -1.09 & 0.10 & 0.84 & 1.09\\\\\n\t 2 & -0.81 & -0.13 & 0.76 & -0.44\\\\\n\t 3 & 2.09 & -1.62 & 0.95 & -0.09\\\\\n\\end{tabular}\n","text/plain":[" subject time1 time2 time3 time4\n","1 1 -1.09 0.10 0.84 1.09\n","2 2 -0.81 -0.13 0.76 -0.44\n","3 3 2.09 -1.62 0.95 -0.09"]},"metadata":{}}],"source":["library(tidyverse) #We'll learn about this package in the next tutorial!\n","\n","long_data %>% # This is a pipe. We will learn about this later\n"," mutate(timepoint = paste0('time',timepoint)) %>% # mutate makes a new column\n"," spread(timepoint, observation) # spread pushes an observation across multiple columns"]},{"cell_type":"markdown","metadata":{"id":"Ig5Hr5dD0ZAh"},"source":["---\n","# Interacting with model objects in R"]},{"cell_type":"markdown","metadata":{"id":"raUZkQY20ZAh"},"source":["Whenever you run a regression or any other type of model, the resulting model is saved in an **object** with properties you can access. This is handy for fitting a model once, and then referencing different aspects of that model's performance and fit. Let's see an example:"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":286},"executionInfo":{"elapsed":169,"status":"ok","timestamp":1706697264939,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"POfAYyZ60ZAh","outputId":"839ecd3a-86fe-4134-e083-456ad793a6a4"},"outputs":[{"output_type":"display_data","data":{"text/html":["\n","\n","\n","\t\n","\t\n","\n","\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\n","
A data.frame: 6 × 3
x1x2y
<dbl><dbl><dbl>
1-4.0-4-0.3820138
2-3.5-4-0.3706878
3-3.0-4-0.3525741
4-2.5-4-0.3241418
5-2.0-4-0.2807971
6-1.5-4-0.2175745
\n"],"text/markdown":"\nA data.frame: 6 × 3\n\n| | x1 <dbl> | x2 <dbl> | y <dbl> |\n|---|---|---|---|\n| 1 | -4.0 | -4 | -0.3820138 |\n| 2 | -3.5 | -4 | -0.3706878 |\n| 3 | -3.0 | -4 | -0.3525741 |\n| 4 | -2.5 | -4 | -0.3241418 |\n| 5 | -2.0 | -4 | -0.2807971 |\n| 6 | -1.5 | -4 | -0.2175745 |\n\n","text/latex":"A data.frame: 6 × 3\n\\begin{tabular}{r|lll}\n & x1 & x2 & y\\\\\n & & & \\\\\n\\hline\n\t1 & -4.0 & -4 & -0.3820138\\\\\n\t2 & -3.5 & -4 & -0.3706878\\\\\n\t3 & -3.0 & -4 & -0.3525741\\\\\n\t4 & -2.5 & -4 & -0.3241418\\\\\n\t5 & -2.0 & -4 & -0.2807971\\\\\n\t6 & -1.5 & -4 & -0.2175745\\\\\n\\end{tabular}\n","text/plain":[" x1 x2 y \n","1 -4.0 -4 -0.3820138\n","2 -3.5 -4 -0.3706878\n","3 -3.0 -4 -0.3525741\n","4 -2.5 -4 -0.3241418\n","5 -2.0 -4 -0.2807971\n","6 -1.5 -4 -0.2175745"]},"metadata":{}}],"source":["# generate data where y is a function of two variables, x1 and x2\n","x1 <- seq(-4,4,0.5) #generate data ranging from -4 to 4 in steps of 0.5\n","x2 <- seq(-4,4,0.5)\n","\n","#specify a sigmoidal relationship between x1 and y\n","#and a linear relationship between x2 and y\n","dat <- expand.grid(x1=x1, x2=x2) %>%\n"," mutate(y = 1/(1+exp(-x1)) + 0.1*x2)\n","\n","head(dat)"]},{"cell_type":"markdown","metadata":{"id":"O5ANePCVEyRf"},"source":["Note that `expand.grid` just creates a data frame with all possible pairs of the input variables. So here, each value of `x1` was paired with an `x2` value of -4, then with an `x2` value of -3.5, etc...\n","\n","We'll learn more about the pipe (%>%) and `mutate` in the next tutorial!"]},{"cell_type":"markdown","metadata":{"id":"DGOIFowS0ZAi"},"source":["Here is how y depends on x1 and x2:"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":497},"executionInfo":{"elapsed":605,"status":"ok","timestamp":1706697298890,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"eK7wZzTg0ZAi","outputId":"76051459-93c0-4197-9074-69ffe45dba40","scrolled":true},"outputs":[{"output_type":"display_data","data":{"text/plain":["plot without title"],"image/png":"iVBORw0KGgoAAAANSUhEUgAABaAAAAPACAMAAAD0Wi6aAAADAFBMVEUAAAABAQECAgIDAwME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\nnzbYNn4ovxsMNIJiMwYah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JTwYLokXN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\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setting figure size\n","options(repr.plot.width=12, repr.plot.height=8)\n","\n","dat %>%\n"," gather(var, value, x1, x2) %>% # make it long format - only x1 or x2 in each row\n"," ggplot(aes(value, y)) + # we will learn aboug ggplot in a later tutorial\n"," stat_summary(geom='point',fun=mean) +\n"," stat_summary(geom='line',fun=mean) +\n"," facet_wrap(~var) # optimally wraps figures as needed\n"]},{"cell_type":"markdown","metadata":{"id":"yZHaRzcg0ZAi"},"source":["Now, let's add some noise and try to fit a regression model"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"P9Wet_zl0ZAi"},"outputs":[],"source":["#create new y_obs variable with normally distributed noise\n","dat <- mutate(dat, y_obs = y + rnorm(length(y), mean=0, sd=0.1))\n","\n","#fit a linear model to find the regression coefficients\n","model_fit <- lm(y_obs ~ x1 + x2, data=dat)"]},{"cell_type":"markdown","metadata":{"id":"0KkyK-Kd0ZAi"},"source":["The resulting model is saved in the `model_fit` variable. This is the \"model object\", and you can do a number of things with it. First, the `str()` command, which is a general function for printing the structure of r objects, will tell you what you can find in the model object. As you can see below, it is a list of different variables, which you can access by typing the name of the model, followed by `$variable`."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":190,"status":"ok","timestamp":1706697309116,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"ho58svUp0ZAi","outputId":"8fb17a48-f287-4913-9f6c-d9b713dd8808"},"outputs":[{"output_type":"stream","name":"stdout","text":["List of 12\n"," $ coefficients : Named num [1:3] 0.4996 0.1507 0.0999\n"," ..- attr(*, \"names\")= chr [1:3] \"(Intercept)\" \"x1\" \"x2\"\n"," $ residuals : Named num [1:289] 0.0767 0.1405 0.0611 -0.0984 -0.0678 ...\n"," ..- attr(*, \"names\")= chr [1:289] \"1\" \"2\" \"3\" \"4\" ...\n"," $ effects : Named num [1:289] -8.4925 6.2743 4.1608 -0.1134 -0.0814 ...\n"," ..- attr(*, \"names\")= chr [1:289] \"(Intercept)\" \"x1\" \"x2\" \"\" ...\n"," $ rank : int 3\n"," $ fitted.values: Named num [1:289] -0.503 -0.427 -0.352 -0.277 -0.201 ...\n"," ..- attr(*, \"names\")= chr [1:289] \"1\" \"2\" \"3\" \"4\" ...\n"," $ assign : int [1:3] 0 1 2\n"," $ qr :List of 5\n"," ..$ qr : num [1:289, 1:3] -17 0.0588 0.0588 0.0588 0.0588 ...\n"," .. ..- attr(*, \"dimnames\")=List of 2\n"," .. .. ..$ : chr [1:289] \"1\" \"2\" \"3\" \"4\" ...\n"," .. .. ..$ : chr [1:3] \"(Intercept)\" \"x1\" \"x2\"\n"," .. ..- attr(*, \"assign\")= int [1:3] 0 1 2\n"," ..$ qraux: num [1:3] 1.06 1.08 1.09\n"," ..$ pivot: int [1:3] 1 2 3\n"," ..$ tol : num 1e-07\n"," ..$ rank : int 3\n"," ..- attr(*, \"class\")= chr \"qr\"\n"," $ df.residual : int 286\n"," $ xlevels : Named list()\n"," $ call : language lm(formula = y_obs ~ x1 + x2, data = dat)\n"," $ terms :Classes 'terms', 'formula' language y_obs ~ x1 + x2\n"," .. ..- attr(*, \"variables\")= language list(y_obs, x1, x2)\n"," .. ..- attr(*, \"factors\")= int [1:3, 1:2] 0 1 0 0 0 1\n"," .. .. ..- attr(*, \"dimnames\")=List of 2\n"," .. .. .. ..$ : chr [1:3] \"y_obs\" \"x1\" \"x2\"\n"," .. .. .. ..$ : chr [1:2] \"x1\" \"x2\"\n"," .. ..- attr(*, \"term.labels\")= chr [1:2] \"x1\" \"x2\"\n"," .. ..- attr(*, \"order\")= int [1:2] 1 1\n"," .. ..- attr(*, \"intercept\")= int 1\n"," .. ..- attr(*, \"response\")= int 1\n"," .. ..- attr(*, \".Environment\")= \n"," .. ..- attr(*, \"predvars\")= language list(y_obs, x1, x2)\n"," .. ..- attr(*, \"dataClasses\")= Named chr [1:3] \"numeric\" \"numeric\" \"numeric\"\n"," .. .. ..- attr(*, \"names\")= chr [1:3] \"y_obs\" \"x1\" \"x2\"\n"," $ model :'data.frame':\t289 obs. of 3 variables:\n"," ..$ y_obs: num [1:289] -0.426 -0.287 -0.291 -0.375 -0.269 ...\n"," ..$ x1 : num [1:289] -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 ...\n"," ..$ x2 : num [1:289] -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 ...\n"," ..- attr(*, \"terms\")=Classes 'terms', 'formula' language y_obs ~ x1 + x2\n"," .. .. ..- attr(*, \"variables\")= language list(y_obs, x1, x2)\n"," .. .. ..- attr(*, \"factors\")= int [1:3, 1:2] 0 1 0 0 0 1\n"," .. .. .. ..- attr(*, \"dimnames\")=List of 2\n"," .. .. .. .. ..$ : chr [1:3] \"y_obs\" \"x1\" \"x2\"\n"," .. .. .. .. ..$ : chr [1:2] \"x1\" \"x2\"\n"," .. .. ..- attr(*, \"term.labels\")= chr [1:2] \"x1\" \"x2\"\n"," .. .. ..- attr(*, \"order\")= int [1:2] 1 1\n"," .. .. ..- attr(*, \"intercept\")= int 1\n"," .. .. ..- attr(*, \"response\")= int 1\n"," .. .. ..- attr(*, \".Environment\")= \n"," .. .. ..- attr(*, \"predvars\")= language list(y_obs, x1, x2)\n"," .. .. ..- attr(*, \"dataClasses\")= Named chr [1:3] \"numeric\" \"numeric\" \"numeric\"\n"," .. .. .. ..- attr(*, \"names\")= chr [1:3] \"y_obs\" \"x1\" \"x2\"\n"," - attr(*, \"class\")= chr \"lm\"\n"]}],"source":["str(model_fit) #print the structure of the model object"]},{"cell_type":"markdown","metadata":{"id":"zgkM2poe0ZAj"},"source":["For example, if we want to extract the estimated regression coefficients, we can type this, which returns a named vector."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"elapsed":189,"status":"ok","timestamp":1706697314936,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"eSP2I1iD0ZAj","outputId":"6e3cef12-6ddb-447b-e66f-fcb446ec8cdc"},"outputs":[{"output_type":"display_data","data":{"text/html":["
(Intercept)
0.499559922079091
x1
0.150675486478537
x2
0.0999191218958173
\n"],"text/markdown":"(Intercept)\n: 0.499559922079091x1\n: 0.150675486478537x2\n: 0.0999191218958173\n\n","text/latex":"\\begin{description*}\n\\item[(Intercept)] 0.499559922079091\n\\item[x1] 0.150675486478537\n\\item[x2] 0.0999191218958173\n\\end{description*}\n","text/plain":["(Intercept) x1 x2 \n"," 0.49955992 0.15067549 0.09991912 "]},"metadata":{}}],"source":["model_fit$coefficients"]},{"cell_type":"markdown","metadata":{"id":"T18PjuC80ZAj"},"source":["If we run multiple models, we might want to store these values in a data.frame, rather than a named vector like this:"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":192},"executionInfo":{"elapsed":157,"status":"ok","timestamp":1706697316463,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"RifpOV1b0ZAj","outputId":"e47338be-8d81-4804-cc44-0633ca8337bf"},"outputs":[{"output_type":"display_data","data":{"text/html":["\n","\n","\n","\t\n","\t\n","\n","\n","\t\n","\t\n","\t\n","\n","
A data.frame: 3 × 2
namevalue
<chr><dbl>
(Intercept)(Intercept)0.49955992
x1x1 0.15067549
x2x2 0.09991912
\n"],"text/markdown":"\nA data.frame: 3 × 2\n\n| | name <chr> | value <dbl> |\n|---|---|---|\n| (Intercept) | (Intercept) | 0.49955992 |\n| x1 | x1 | 0.15067549 |\n| x2 | x2 | 0.09991912 |\n\n","text/latex":"A data.frame: 3 × 2\n\\begin{tabular}{r|ll}\n & name & value\\\\\n & & \\\\\n\\hline\n\t(Intercept) & (Intercept) & 0.49955992\\\\\n\tx1 & x1 & 0.15067549\\\\\n\tx2 & x2 & 0.09991912\\\\\n\\end{tabular}\n","text/plain":[" name value \n","(Intercept) (Intercept) 0.49955992\n","x1 x1 0.15067549\n","x2 x2 0.09991912"]},"metadata":{}}],"source":["#store the coefficients in a variable\n","coef <- model_fit$coefficients\n","\n","#save the name/value of the coefficients in a dataframe\n","data.frame(name = names(coef), value = coef)"]},{"cell_type":"markdown","metadata":{"id":"AbWkCc8P0ZAj"},"source":["You can also extract the prediction of the model. They are stored under `$fitted.values`, or you can get them by typing `fitted(model_fit)`, which returns the same values. Then, we can plot the observed values against the predicted values:"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":286},"executionInfo":{"elapsed":162,"status":"ok","timestamp":1706697318858,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"xaG8BE1u0ZAj","outputId":"68bac0cb-895b-4487-beca-48c9568a98df"},"outputs":[{"output_type":"display_data","data":{"text/html":["\n","\n","\n","\t\n","\t\n","\n","\n","\t\n","\t\n","\t\n","\t\n","\t\n","\t\n","\n","
A data.frame: 6 × 5
x1x2yy_obsfitted
<dbl><dbl><dbl><dbl><dbl>
1-4.0-4-0.3820138-0.4261378-0.5028185
2-3.5-4-0.3706878-0.2869985-0.4274808
3-3.0-4-0.3525741-0.2910417-0.3521430
4-2.5-4-0.3241418-0.3752198-0.2768053
5-2.0-4-0.2807971-0.2692938-0.2014675
6-1.5-4-0.2175745-0.2070880-0.1261298
\n"],"text/markdown":"\nA data.frame: 6 × 5\n\n| | x1 <dbl> | x2 <dbl> | y <dbl> | y_obs <dbl> | fitted <dbl> |\n|---|---|---|---|---|---|\n| 1 | -4.0 | -4 | -0.3820138 | -0.4261378 | -0.5028185 |\n| 2 | -3.5 | -4 | -0.3706878 | -0.2869985 | -0.4274808 |\n| 3 | -3.0 | -4 | -0.3525741 | -0.2910417 | -0.3521430 |\n| 4 | -2.5 | -4 | -0.3241418 | -0.3752198 | -0.2768053 |\n| 5 | -2.0 | -4 | -0.2807971 | -0.2692938 | -0.2014675 |\n| 6 | -1.5 | -4 | -0.2175745 | -0.2070880 | -0.1261298 |\n\n","text/latex":"A data.frame: 6 × 5\n\\begin{tabular}{r|lllll}\n & x1 & x2 & y & y\\_obs & fitted\\\\\n & & & & & \\\\\n\\hline\n\t1 & -4.0 & -4 & -0.3820138 & -0.4261378 & -0.5028185\\\\\n\t2 & -3.5 & -4 & -0.3706878 & -0.2869985 & -0.4274808\\\\\n\t3 & -3.0 & -4 & -0.3525741 & -0.2910417 & -0.3521430\\\\\n\t4 & -2.5 & -4 & -0.3241418 & -0.3752198 & -0.2768053\\\\\n\t5 & -2.0 & -4 & -0.2807971 & -0.2692938 & -0.2014675\\\\\n\t6 & -1.5 & -4 & -0.2175745 & -0.2070880 & -0.1261298\\\\\n\\end{tabular}\n","text/plain":[" x1 x2 y y_obs fitted \n","1 -4.0 -4 -0.3820138 -0.4261378 -0.5028185\n","2 -3.5 -4 -0.3706878 -0.2869985 -0.4274808\n","3 -3.0 -4 -0.3525741 -0.2910417 -0.3521430\n","4 -2.5 -4 -0.3241418 -0.3752198 -0.2768053\n","5 -2.0 -4 -0.2807971 -0.2692938 -0.2014675\n","6 -1.5 -4 -0.2175745 -0.2070880 -0.1261298"]},"metadata":{}}],"source":["#extract model estimate of y for each x and store in df as fitted\n","dat$fitted <- model_fit$fitted.values\n","\n","head(dat) #we see \"fitted\" column added"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":497},"executionInfo":{"elapsed":521,"status":"ok","timestamp":1706697320991,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"HmA3jL8R0ZAk","outputId":"af0ca8ff-e914-49d5-81b3-f6e8f867573d"},"outputs":[{"output_type":"display_data","data":{"text/plain":["plot without title"],"image/png":"iVBORw0KGgoAAAANSUhEUgAABaAAAAPACAMAAAD0Wi6aAAADAFBMVEUAAAABAQECAgIDAwME\nBAQFBQUGBgYHBwcICAgJCQkKCgoLCwsMDAwNDQ0ODg4PDw8QEBARERESEhITExMUFBQVFRUW\nFhYXFxcYGBgZGRkaGhobGxscHBwdHR0eHh4fHx8gICAhISEiIiIjIyMkJCQlJSUmJiYnJyco\nKCgpKSkqKiorKyssLCwtLS0uLi4vLy8wMDAxMTEyMjIzMzM0NDQ1NTU2NjY3Nzc4ODg5OTk6\nOjo7Ozs8PDw9PT0+Pj4/Pz9AQEBBQUFCQkJDQ0NERERFRUVGRkZHR0dISEhJSUlKSkpLS0tM\nTExNTU1OTk5PT09QUFBRUVFSUlJTU1NUVFRVVVVWVlZXV1dYWFhZWVlaWlpbW1tcXFxdXV1e\nXl5fX19gYGBhYWFiYmJjY2NkZGRlZWVmZmZnZ2doaGhpaWlqampra2tsbGxtbW1ubm5vb29w\ncHBxcXFycnJzc3N0dHR1dXV2dnZ3d3d4eHh5eXl6enp7e3t8fHx9fX1+fn5/f3+AgICBgYGC\ngoKDg4OEhISFhYWGhoaHh4eIiIiJiYmKioqLi4uMjIyNjY2Ojo6Pj4+QkJCRkZGSkpKTk5OU\nlJSVlZWWlpaXl5eYmJiZmZmampqbm5ucnJydnZ2enp6fn5+goKChoaGioqKjo6OkpKSlpaWm\npqanp6eoqKipqamqqqqrq6usrKytra2urq6vr6+wsLCxsbGysrKzs7O0tLS1tbW2tra3t7e4\nuLi5ubm6urq7u7u8vLy9vb2+vr6/v7/AwMDBwcHCwsLDw8PExMTFxcXGxsbHx8fIyMjJycnK\nysrLy8vMzMzNzc3Ozs7Pz8/Q0NDR0dHS0tLT09PU1NTV1dXW1tbX19fY2NjZ2dna2trb29vc\n3Nzd3d3e3t7f39/g4ODh4eHi4uLj4+Pk5OTl5eXm5ubn5+fo6Ojp6enq6urr6+vs7Ozt7e3u\n7u7v7+/w8PDx8fHy8vLz8/P09PT19fX29vb39/f4+Pj5+fn6+vr7+/v8/Pz9/f3+/v7////i\nsF19AAAACXBIWXMAABJ0AAASdAHeZh94AAAgAElEQVR4nOzdebwV8+PH8Wm77UoqWZIkyV4p\na5S1iLKkvqGFZIuyRZKtiBAK2bOGCCUhFUVpV1pve7e7n+/Xz76UnN+Z+czZ7j2fOTPvmc+Z\nufe+X3/43jkz85lPfb+Pp/OdO4sWZowxFsg0vyfAGGMsdQSaMcYCGoFmjLGARqAZYyygEWjG\nGAtoBJoxxgIagWaMsYBGoBljLKC5BfqXH131957/czeAun75y+8ZSPtzz09+T0HWT3/7PQNp\nf+z52e8pyPq/XX7PQNrve371ewrSdvs9AWm/7fnN1f4/eQb0TyFX7Qr/190A6vrpL79nIO2v\n8I9+T0HWj7v8noG0P8L/5/cUZP13t98zkPZb+Ge/pyBtj98TkPZr+FdX+/9IoNNGoJEINBKB\nhiLQBDqQEWgkAo1EoJEItPoINBKBRiLQUASaQAcyAo1EoJEINBKBVh+BRiLQSAQaikAT6EBG\noJEINBKBRiLQ6iPQSAQaiUBDEWgCHcgINBKBRiLQSARafQQaiUAjEWgoAk2gAxmBRiLQSAQa\niUCrj0AjEWgkAg1FoAl0ICPQSAQaiUAjEWj1EWgkAo1EoKEINIEOZAQaiUAjEWgkAq0+Ao1E\noJEINBSBJtCBjEAjEWgkAo1EoNVHoJEINBKBhiLQBDqQEWgkAo1EoJEItPoINBKBRiLQUASa\nQAcyAo1EoJEINBKBVh+BRiLQSAQaikAT6EBGoJEINBKBRiLQ6iPQSAQaiUBDEWgCHcgINBKB\nRiLQSARafQQaiUAjEWgoAk2gAxmBRiLQSAQaKdNA597WPfrjTRdE6kmg/YxAIxFoJAKNlGGg\n5/d9Mgb0gE8i+/+PQPsZgUYi0EgEGinDQM8p/i4G9KVLk1YRaB8i0EgEGolAI2X8HHQM6F0X\njB9y1cO5+o95UyPt+NVV/4R/czeAuv7Y7fcMpO0O/+73FGT9/o/fM5C2K/yH31OQ9dsev2cg\n7e/wn35PQdq/fk9A2l/hv1zt/xsM9E9XjsvOvv9KfYC57SIttrc/Y4wxe+2J/eQUaKM/es4K\n8xu0f/EbNBK/QSPxGzSSf9+gRTdMjv7Ec9A+xHPQSDwHjcRz0Ej+nYPePmF3OPxnz7kE2scI\nNBKBRiLQSBkG+sfQrO6h0J/hWdPDv/R5siD34QF/EWgfI9BIBBqJQCNlGOir9ZtTLpgWHntP\nOLzlnl5XjCqMrSLQPkSgkQg0EoFGWt6/3dnPFuP781bv9BFoJAKNRKChAgv0zOpapH74AAQ6\nfQQaiUAjEWiowALdUjOaDg9AoNNHoJEINBKBhgoq0GuFz9oweAQCnT4CjUSgkQg0VFCBXkOg\nMxCBRiLQSAQaKqhAhw7lKQ71EWgkAo1EoKECC/Snxi8Jr8AHINDpI9BIBBqJQEMFFujQsr7H\nnTGBl9kpjUAjEWgkAg0VXKD5yiv1EWgkAo1EoKEINIEOZAQaiUAjEWgkAq0+Ao1EoJEINBSB\nJtCBjEAjEWgkAo1EoNVHoJEINBKBhiLQBDqQEWgkAo1EoJEItPoINBKBRiLQUASaQAcyAo1E\noJEINBKBVh+BRiLQSAQaikAT6EBGoJEINBKBRiLQ6iPQSAQaiUBD+Qn0tDEvZ8vXEmj1EWgk\nAo1EoKH8A3rrKZqm7f2WdD2BVh+BRiLQSAQayj+gexnPe677vWw9gVYfgUYi0EgEGso3oHOq\niSfyPyDbgECrj0AjEWgkAg3lG9A/mO+0GizbgECrj0AjEWgkAg3lG9D5dQXQT8o2INDqI9BI\nBBqJQEO5BDoP33Wk4XOL7bL1BFp9BBqJQCMRaCg3QK/vvVeVVpPQvYvuqKFpJy+SrifQ6iPQ\nSAQaiUBDuQA67zjjOzAsdChv/jqLtQRafQQaiUAjEWgoF0CPFyeRD3DxYlerCLT6CDQSgUYi\n0FAugL7WvA5jo3ezSYxAq49AIxFoJAIN5QLo24TPVXK9m01iBFp9BBqJQCMRaCgXQM8VQJ/n\n3WSSItDqI9BIBBqJQEO5uYrjAd3nQ6x+0ecmAq0+Ao1EoJEINJSr66C/HjbwaRdXQltHoNVH\noJEINBKBhuLzoAl0ICPQSAQaiUAjEWj1EWgkAo1EoKEINIEOZAQaiUAjEWgkAq0+Ao1EoJEI\nNBSBJtCBjEAjEWgkAo1EoNVHoJEINBKBhiLQBDqQEWgkAo1EoJEItPoINBKBRiLQUASaQAcy\nAo1EoJEINBKBVh+BRiLQSAQaikAT6EBGoJEINBKBRiLQ6iPQSAQaiUBDEWgCHcgINBKBRiLQ\nSARafQQaiUAjEWgoAk2gAxmBRiLQSAQaiUCrj0AjEWgkAg1FoAl0ICPQSAQaiUAjEWj1EWgk\nAo1EoKEINIEOZAQaiUAjEWgkAq0+Ao1EoJEINJQjoFdcvF+Ti5apmkqJCLT6CDQSgUYi0FBO\ngF7XSIu0z2plk0mKQKuPQCMRaCQCDeUE6AGaUR9lk0mKQKuPQCMRaCQCDeUE6OME0K2VTSYp\nAq0+Ao1EoJEqCtBTbhz4QpF3wzkB+gQBdBvvjm4VgVYfgUYi0EgVBOjeOpHtcz0bzwnQIwXQ\nd3l2cMsItPoINBKBRqoYQE8URt7k1XiOgM4/WT92hzzPDm4ZgVYfgUYi0EgVA+huAujmXo3n\n7DK7wgm9ez1d6NmxrSPQ6iPQSAQaqWIA3VkA3dir8XijCoEOZgQaiUAjeQj0zQLoM70aj0AT\n6GBGoJEINJKHQGfvr/tcY75X4yUDXfxc232OfdLDa0TcRKDVR6CRCDRSxQA6tLRb3eqnfO7Z\ncMlAi8s0hno3upsItPoINBKBRqogQEfy9Ld0iUBvqCZOoCz18gBwBFp9BBqJQCNVHKA9LRHo\nKcJn7UXfZpMYgVYfgUYi0EgEGioR6Gkm0K/7NpvECLT6CDQSgUYi0FCJQOfsY/hcN9u32SRG\noNVHoJEINBKBhkr6JeHk6hGfs4JxhoNAZyACjUSgkQi0nQqe6HHBQ4n3aidfB734xq7XfuPh\n4Xa4uGSPQKuPQCMRaCQCbaOCk/RzGEfmxD9ReaPKMwdpNXuuRfcm0Ooj0EgEGolA2+h+8VvA\nwfFPFAL9rHGsY9FnKxFo9RFoJAKNRKBt1LHUI/fVAV3UWBxsPLg/gVYfgUYi0EgE2kYnCjNb\nxD9RB/QG86K968H9CbT6CDQSgUYi0DYaLMzsHf9EHdA5VcTB7gT3J9DqI9BIBBqJQNtoc1Od\nzAYJ7+VWeA76PMPn6uiDnQi0+gg0EoFGItB2Wtuv+UG9ViR8oBDodS31q6ofRXcn0Ooj0EgE\nGolAQ1kCnT+q/aEXfAWPnffsjSO/g/cm0Ooj0EgEGolAiz6+9taZDja3BFq8YGuGyxmBEWj1\nEWgkAo1EoPW2Hq6Ter79G/isgJ4sfsvX0v20kAi0+gg0EoFGItB6JwlTH7C9gxXQQ8wL5fx5\neBKBVh+BRiLQSAQ60grN6Vu/rYC+1Rxtk/uJARFo9RFoJAKNRKAjfWSSWt/2HlZATxeDtXU/\nLyQCrT4CjUSgkcow0HmevaZ1gQn0Mbb3sPwl4dX6WLW9e0Otowi0+gg0EoFG8hPovBWW7wm0\nBvr9o6vUOG+ZRzNpa/hcabrtHayvg57Uo+N1q9zOCYxAq49AIxFoJP+Azu5ZRat5S758A0ug\nZxikNt3szVxW6jeHVHvE/g4qHzfqLgKtPgKNRKCRfAO66LSSj/AsmSXQ7cVJiWFezWbaQy87\necAngSbQgYxAIxHo0n0ghK0ivxjNEujaYvduCmZmJwJNoAMZgUYi0KV7xPzF3GfSLSyB3rfU\nA+YyGoEm0IGMQCMR6NK9aAK9WLqFJdDXiL3fVTAzO3kK9MapH3p0Lj1EoDMRgUYi0Ei+Ab2p\nkSFse/kWlkDntEtzBlttXgL9SG1Nq/u4V6MRaPURaCQCjeTfVRxTG0SEPXS5fAPry+yKXrrh\ndvnpEdV5CPQU8f8FPvBoOAKtPgKNRKCRfLwOeuOEuydZXTlRZh836qwzBdDneDQcgVYfgUYi\n0Ehl+E7C5CYP6juhQNlcSuYh0K0F0Ed4NByBVh+BRiLQSOUF6F46csftUDeb5DwE+gx+g04Z\ngUYi0EgEGskJ0C8I5a5VOJ2kPAT6PZ6DThmBRiLQSAQayQnQ3YVyTRVOJykvr+IYU1vT6oz1\najQCrT4CjUSgkcoJ0GcLoBsonE5S3l4H/f4H3j07mkCrj0AjEWikcgK0+ZD8zgqnkxTvJCTQ\ngYxAIxFoJCdAb26q+1wjY89gdgd03jfrPJpH6YID9F+7XPVv2N3+Ctu9x+8ZSNsT3u33FGTt\n/tfvGUgL8N/aruD+rf0T/sf+xlt6N6h9xkJ1kymRm7+1vx+srWknrfJsLsk5+ltL0d+eAf3L\n/7lqd/gndwOo69e//Z6BtL/DP/s9BVm/7PZ7BtL+Cv/q9xRk/fSP3zOQ9mf4N7+nIG2Pi33F\nY6Ka7fBsMkn9Hv7d1f4/ewY0T3H4EE9xIPEUB1I5vZOwqIE4Xz7G5vYbb2jbfuhW28MH5xQH\ngfYhAo1EoJHKKdAbzcf4DbS3+Sbj7Pqh2+0OT6DVR6CRCDQSgYZyAXR+dQH0cHubDxRbD7E7\nPIFWH4FGItBIBBrKzVUc/Qxxay21t/URWrrHsiZHoNVHoJEINBKBhnID9I5OEXD3etXm1kcS\n6MBFoJEINBKBhnJ3HfSMMS+ut7vtdQLo2+xuT6DVR6CRCDQSgYbK3J2EW5vrPrfOsbs9gVYf\ngUYi0EgEGmrXlowdauvtp3Ycbv85qgRafQQaiUAjBRfoxZcecuQN3r1M1Wk7i+Tr1l5aQzvg\nyczNxUkEWn0EGolAIwUW6CV1jPeM5Ppz9NdbVarZfaVkZX4b47TwUxmdkd0ItPoINBKBRgos\n0OeIX47d58vB3zGO3VJyYmGi+WzTwsxOyl4EWn0EGolAIwUWaPOG6PN8Ofhh4uCjUq8dat4L\nuCqzk7IXgVYfgUYi0EiBBbqxQPBCP46dX0kc/D+pV48Uayvbf0BGBiPQ6iPQSAQaKbBA9xYK\njvfj2MW1LF9xuKiGsfbchI+2BQZrAq0+Ao1EoJECC3S28ZCgc4p9Obj5b4dPJauf0h+n0XJt\nbHnmcZp25MeZmVq6CLT6CDQSgUYKLNChbfd1v3iCxbVuKtt8lO7z3dL1Sx+7eWJ+bElccFIz\nY69zsYxAq49AIxFopOAC7euNKgXPXz98rsX6pDsJze/b56udks0ItPoINBKBRiLQUElAtxVA\nH+rXZJIi0Ooj0EgEGqncAp39zH1vq7tQOQnozgLo45UdzUkEWn0EGolAI5VXoCfXj5B51Nr0\nG2IlAf2Ms3dYqY1Aq49AIxFopHIK9Nr6hplnxT6Y1L7hMY969406+Wl2xiP4L/XngpOSEWj1\nEWgkAo1UToF+XHyprRR97PJYJ68BtFGJx41+ds+ITzwb210EWn0EGolAI5VToEeYd2N/Kxa3\n1RSLnl0Jl7nnQTuNQKuPQCMRaKQAA/3TkncWoftOEiBXN59zP9P02rNHhBJoAh3ICDQSgQaa\nr7+N73zwFmrziaB3mouzTaCftbl78XPntOvzncUGBJpABzICjUSgnbfDeNWTdim4+6rzKmm1\nhkV/K5i/vzFYzR9s7t3f+Po9U74BgSbQgYxAIxFo571c4td8jtu+pCC+8FENJ2c4Zohjt5Rv\nQaAJdCAj0EgE2nkPmGcl5ngz3PLB51492+7Gd5nHXi3dgkAT6EBGoJEItPPMb9CVN/hw7CjQ\n8jMiBJpABzICjUSgnZfTwjCylx/Hni58biHfgkAT6EBGoJEINND8YyJGXrDNl2NfofucNUO+\nAYEm0IGMQCMRaKSfl7+71KdDF03ofPRl31psQKAJdCAj0EgEGknx40ZdvQuAQBPoQEagkQg0\nkkqgt17bqGrrF/H9CTSBDmQEGolAIykEuqiT8VvACfAABJpABzICjUSg7VWQtKQQ6DfFZRp7\n56ffNHUEmkAHMgKNRKBttKL7XlntpyV8oBDo6IXOS9EBCDSBDmQEGolAp29rM+P5F5/HP1EI\n9IMm0OvQAQg0gQ5kBBqJQKfP/FLbIf6JQqC/q24c7AR4AAJNoAMZgUYi0OnrJoCuFf9E5VUc\nj2ZFjtVkKbw/gSbQgYxAIxHo9PUSQDeOf6L0Ouj5t135sIu7FAk0gQ5kBBqJQKfPvLDi6vgn\nim9UcRWBJtCBjEAjEWgbDdR9PmZ7/AMCjUSg1UegkQg0ko9Af33W3vv3WRNfnnbz1c8lXgkd\nIKBn9+pwceIVgASaQAczAo1EoFP0bS39K3Nz+Yng4AD9qnH2ZUzCJ2mA/mHKl3lKZySPQKuP\nQCMRaCT/gD5LnHS+Q7pBYIDeUV+8Ijzh+f2WQBcOrKJpB3+ielqpI9DqI9BIBBrJP6AbCqDP\nkm4QGKA/MW9rSXi4kiXQ4pLuBmustlEWgVYfgUYi0Ej+AX2gUO8C6QaBAfpjE+jn4x9ZAV0s\nvnBr9yifWKoItPoINBKBRvIP6IGCsWekGwQG6K3G2XKt2or4R1ZAbzU97698Yqki0Ooj0EgE\nGsk/oLe11hXrUSzdIDBAh542wL07/sG00+o0HbhJsnXxXgLoERmZW8kItPoINBKBRvLxMru8\nsb37vmaxPjhAh6aec1jnSfFFcc6jnexhpbcaq+uvysjUSkag1UegkQg0UnBuVClVgIAuUWvx\nFflJyeqCyyMrD5ia0SnFItDqI9BIBBqJQDsv1zzJ3E+6xYo3PtmZwQklRqDVR6CRCDQSgXZe\nYTUB9HV+TyRVBFp9BBqJQCMRaKDzBNAf+z2PVBFo9RFoJAKNVH6B3qTuZus1xjXcg5WN7yYC\nrT4CjUSgkcor0JMO1qp2/g7fP09++V+kHU9cNvBDfHCVEWj1EWgkAo2UQaBzxg0audTB9m6A\nnmKcgzhgI7j720dUqd3D6jI5Ps2OQAcyAo1EoCMt088LVH/O/g5ugD5anCUeJltfPPnOUQuk\ne79v7Nxyh3x8Ak2gAxmBRiLQkU4Q7xxckX5LMzdAZwmgL5Sszjk5sjLrXtne5nXOD8jHJ9AE\nOpARaCQCHQqtNi8eHpN+UzM3QDcSB+srWX2NWP1p6rWFlcXqXvLxCTSBDmQEGolAh0LfaU6f\nUOEG6OusL4RrIFZfLVldR6weKB+fQBPoQEagkQh0KJRrqve27T12/lAIH22nfg5DGy5ZW1xV\nzOViyfo+YvU0yeoQgSbQAY1AIxHoSGMM9E4rsrn5D+doWrVr49cyZw88ZP9u8t/rhULff7go\n4dK44sl33Dc/eYME7s2TzHeHUrflSH2t/F0vBJpABzQCjUSgIxU/3lSr21/2jM6SFRxvEDoo\nupzTSl+sLb2yeWuPyOoOS6XjLe5ap/rJn0eXJhuDHyidTMFz197xpdX0CDSBDmQEGolAi7Zv\ntvv92SRUq5JtLt8jls+UbX+psfpI2d2DG/bVV9eMfad+qalWpZOL+1gINIEOZAQaiUDrFT/U\nWKt5pc17Rx4yf6c4y1w2H39RX7J59BqRtyTrbxCrz45/ku3qcXMEmkAHMgKNRKD17jeM7Gjv\nS/Tzprjfm8s9xGJjyeYz01zEd7pYvZ/TOcsi0AQ6kBFoJAIdKaemk8s4NjcxNu4UXZ4gdr5c\nsvn3JtCyN7SYX8APdThnaQSaQAcyAo1EoCN9Yxpq82XXn+hnjY9ZHV0sNohtLv21Xhdj7ENy\nJKufFcce6mjGFhFoAh3ICDQSgY70gwn04za33/b2Ux8lnA4pnnhZt/tl/oZCG06LDN1qnnR9\nL/3QJ3r2BFICTaADGYFGItB6Jxo+17H9LlWHdxLOfXFGgcXqKYMHvmT7GpK0EWgCHcgINBKB\n1lt+kH6l2yu2tw/uG1UINIEOaAQaiUAb7Zxw0+iV9jcn0EgEWn0EGolAI5XXN6oojkAT6EBG\noJEINBKBRiLQ6iPQSAQaiUBDEWgCHcgINBKBRiLQSARafQQaiUAjEWgoAk2gAxmBRiLQSAQa\niUCrj0AjEWikAAE9+cSGRz2QH18m0EgEWn0EGolAIwUH6OeMGw17xz8g0EgEWn0EGolAIwUG\n6Lz64lEdM2OfEGgkAq0+Ao1EoJECA/R881lKo2KfEGgkAq0+Ao1EoJECA/QiE+hHY58QaCQC\nrT4CjUSgkQIDdHELw+fqS2KfEGgkAq0+Ao1EoJECA3Toi1o60A/FPyDQSARafQQaiUAjBQfo\n0A9Duw74LGGZQCMRaPURaCQCjRQgoEtGoJEItPoINBKBRiLQUASaQAcyAo1EoJEINBKBVh+B\nRiLQSAQaikAT6EBGoJEINBKBRiLQ6iPQSAQaqSTQBYu3+DOR0hFoJAKtPgKNRKCRkoEuGl5L\n085Y4ddkkiPQSARafQQaiUAjJQN9r3E3X+udfs0mKQKNRKDVR6CRCDRSEtB5dcTzMCb4Np3E\nCDQSgVYfgUYi0EhJQH9vPrBoqG/TSYxAIxFo9RFoJAJto4KHOh71n6UJHyQBva2KAHp0hmeV\nOgKNRKDVR6CRCHT6irvo/tacH/8k+Rx0d8PnuiszPa+UEWgkAq0+Ao1EoNP3qviG3D7+STLQ\nG9tF1tZ7PdPTSh2BRso00Lm3dY/++OsT/fo8UESg/YxAIwUG6IEC6Ep5sU9KXAddNOWBZzc4\nGHDz/ByPplY6Ao2UYaDn930yBvSoO7fmPXbjHgLtYwQaKTBAXyOAriwF2lnrumla1YGqLsoj\n0EgZBnpO8XdRoEMXbol8i+6xkkD7GIFGCgzQrwugT4p/4gboolOM0frK1n8/cuCYzfjwBBop\n4+egY0AvvOTfyD8Hv0egfYxAIwUG6NCFuqh1FsQ/cAP0R+YJk9WpV79RM7Ky4Vfw8AQayT+g\nP++v/3PEi5F/fNM50rJ/XRUOu9tfZcGdGv/WkILzt/bPi+efPHhH4icupvaCedn0VynXFu8t\nbkv8Bx7femrFkx75eBc8tssC819o6VxO7R8c6AExoJdeEWnVblf9G3a3v8L++dfvGUj7N/yP\n31OQFeC/tT3B/Vvb7eJvbYAJ9JqUa98y1y6XDzDzgUdXyNda/6190iAy9tE77M3U84KLx57w\nHlf774KBXiROcbwfXcFTHD7EUxxIwTnFUSo3pzjqC4EbpF47zgR6hmz3vDP11bdJh7c8xbFO\nfD/vbHuy3sZTHKWB/t+Fm8Lhn7uvIdA+RqCRyifQc02Bj029+nOxttpG2f63ig3ek623BPop\n8+CS89+qI9BmP4ZmdQ+F/gzPmh4Ojxm6Nff+W/8l0D5GoJHKJ9ATTCPPkazvYay9S7p/M7H7\nZbL1lkDfax58vnwTlRFos6sv0JsWHntPOPz7k30vfzi+P4H2IQKNVD6BfsU08lXJ+h03N9AO\nfKhQur95huRs2XpLoF8SO2dttztbbyPQ6SPQPkSgkcon0Nn1DCP3LZBvYnkPS3th7E2y9VZA\ni4eKaNrtNuapIgJNoAMZgUYqn0CHXqsRIbL+5+ju0wxiG62TrbcC+kPzBPdW9OAuI9AEOpAR\naKRyCnRo+V2X3+fkyR0levMQrfLJ8pPIVkCPMk+vfI0f3VUEmkAHMgKNVF6Azh1//b2LvTz6\nxh3xnwvfefDFTYkrrYB+wgR6mZezcRCBJtCBjEAjlVmg1w88tt3Q2GmEVQdHSKz+tJqJrDla\nv6T6/YRPrID+vpbh89Fq5pI+Ak2gAxmBRiqrQK9voit4ePSJop0NFGt4+h061pnippeEMyaW\nV3E8k6Wfv/5WyVRsRKAJdCAj0EhlFejLxXmEO8TSpkpi8T4V81hjnrN4Kv6R9cOSFt3Z76Et\nKmZiKwJNoAMZgUYqq0AfItA8RSxFXyl7q4p5zDcHHxn/iE+zQyLQ6iPQSAQayRLoQwWaHcVS\ngXj8hfayinlsyxKDJ7xui0AjEWj1EWgkAo1kCfRVAs0R5qJ4/FEHixtTkit+/eY7pI9KKtlQ\nY/C2+fFPCDQSgVYfgUYi0EiWQG8+SEfzuNgLsp46SKvdJ9vu0Hmn6XtfbXPr/KHVNa3rqoRP\nCDQSgVYfgUYi0EjWl9ltva1j5/tyEz7YUWx/aPNpda/Y3T5vYfIv/Qg0EoFWH4FGItBIru4k\ntK6FALobuj+BRiLQ6iPQSAQaSSHQjQXQndD9CTQSgVYfgUYi0EgKge4kgL4B3b8k0HkL/Lvu\nuWQEmkAHMgKNVG6BzrO6omN2dd3nxuvRwZOBzruxmqadvwYdzOMINIEOZAQaqZwC/Wm7qlmd\nv5Gv//i4KllnLICHTwb6eofX+KmNQBPoQEagkcon0PP1x0Fr+1i9FdDyG3a6koDeWFWcMHnH\nxYAeRqAJdCAj0EjlE+hzBJkDPZxNUklAzzZvBR+l6mjOItAEOpARaKTyCXRTQeZJHs4mqSSg\nV5hAT1R1NGcRaAIdyAg0UvkEurUg81wPZ5NU8jlo47ZErfEm6eYZjUAT6EBGoJHKJ9DDBdDP\neTibpJKBXnWk7vM0VQdzGIEm0IGMQCOVT6DzjQf4X269jYNbw0tW4jrowncefNmvd8SWikAT\n6EBGoJHKJ9Ch4jdvuuXjpE/WTV9clLD4SftqtbouQYfnnYRIBFp9BBqJQCN5eSdh7pX6A0Pj\nFz7PMe5U2d/24+9KVBLoH16egF9U7XEEmkAHMgKNVEGAHmSck24Re1P36eIk9RBwuBJAP1oz\nMlY/F6dMvIxAE+hARqCRyg7Qcye8tw0dals1AfKz0Q8aiuUzwPGSgf5UDDYanZ23EWgCHcgI\nNFJZAXqHfu9Jkw/AoRaalyrfGf2gmVjuDo6XDPR/xGCHgYN5HIEm0IGMQCOVFaCvNAxsAD6R\naFMVYWjsxdw3pXli/3s9TrjiW/l4yUCfJQarj83N6wg0gQ5kBBqpjAC903xx60PgWD2NvZts\njC7ndtCX+8k2v1tfm/W+dLhkoAeKubUB5+ZxBJpABzICjVRGgF5lnqO4CRxry5mRnZvOjH9Q\n9NJ1Qz6Wbf2dOFgT6fOUku2PdlMAACAASURBVIFeUsfY/A1wbh5HoAl0ICPQSGUE6Lxawswn\n4NG+em5qbvqtRI+b/zqYJ9ugxFUcU5trWv3H4al5G4Em0IGMQCOVEaBDtxtiHpSZF5eMNYH+\nSrZByeugCxd/lSfZNOMRaAIdyAg0UlkBuuC6app23PzMHHme8LmBFF3eSYhEoNVHoJEINFKJ\n66A3zVxaJNkSKNvyu/gNBtCTpOvTAZ2/cBU2LQ8i0AQ6kBFopLIDtJe93VzT2s6Sry9+9rSW\n530qX58G6Mfqa9oRn6OTcxmBJtCBjEAjlRug8+ZO35h+K9FM40kc9b93Picza6BfESdIfoCH\ndxWBJtCBjEAjlRegPzpI07Jusfk4DPGEfe0q26MXPd29y/CEG82tgTZfFzDU9vCeRqAJdCAj\n0EjeAr19lYdPDEoHdNH6+M/f1zNMHGNv5P2EoKfanUnx2frmTTfEPrAG2ryp5gK7w3sbgSbQ\ngYxAI3kJ9NLOlbS9LYycNubF9fK1pbIGeuvAGlq9YdHrLG4TJh5gb+TWDgUdL7a/LPaBNdAH\nOP2C7mkEmkAHMgKN5CHQOw41XBonWb29Y2TlXtKnX5TOGuhuxsFuMJd6mVcuS+/9S+pesfGb\ndmfSQ2y/T+wDa6CHGVtXt/glpMoINIEOZAQayUOgHxOMNZRcDHeFsbbWUtvjzXjovi+lKz8X\nB6tsPj1piFisae9CvMIL9Y3tPwxa/MtAqxf7wBroAh30mn7dWUigCXQgI9BIHgI9yPwWm/o1\nJXnmmdnhNkcrulTfeqBs9QTzYB+KxUU1xOK9Nkeffs8o6X3cpXtADH527IN010F/OfZZ3y6E\nJtAEOpARaCQPgb5LMJaV+v67bFPUa2yO9rDY/HnJ6tfN4eaay+eJxf2cTtpWefpru7U6i2Mf\n8E5CJAKtPgKNVDGA/k58i+2Vem1RA0HoIzZHays2P1OyektjY/Xh0XMal4rNK8nOcaz6YF6h\nzSOnOtrgI5pdmvCKWQKNRKDVR6CRKgbQoWf0V/O1l91D/ZAhaLOtNgc7RIjbTrZ+an39C3Ps\n4RxDxeZNU2+c2zuy7sivbR46fQQaiUCrj0AjVRCgQ6vGjXhXeiF08Yhamnai7ZdfdxHi9pFu\nkP3Y0PGxl8CGJonNJRf5iUfqH2T3Xw5pI9BIBFp9BBqpogCdprxvHVwGPdf4pWKll2xu3lIA\n/VnKldvNX1A+bf/w1hFoJAKtPgKNRKCdt0m8puRAe89Z/sH8neGIlGsXm2tv92pyBBqJQKuP\nQCMRaOdFL9OYmX7TSN9rVhfxba0q1sruoXEcgUYi0Ooj0EgE2nkTTXLft7V18UFi6+mpV4ub\nZPaz/bi7dBFoJAKtPgKNRKCd940Qt6rN09ZTLX+luOP8yMrmqU9QIykFes45+x56I/5uLwJN\noAMZgUYKLNCh/ga5w+xuPqf7YR3Hye/0XvDqDA/fGqgS6NnGw6rb5qP7E2gCHcgINFJwgc4b\neXCVFo9K7y6Zf123m1dkcj6JqQS6vfi/DmPR/Qk0gQ5kBBopuECH/rvb4uHSz+tXztX4IHOz\nSUoh0EXmLzR7owMQaAIdyAg0UiaBXvLwHa87eO9rzppc6boN4iK8fT08beEkld+gawqg+6L7\nE2gCHcgINFIGgX5M/9LbZrPNrTf1rqRVvWqHZO2r5jUeFi92VZlKoC8QfzLbD6suGYEm0IGM\nQCNlDuh5xi+/El5LYlnxuZb/Rz96Ed5Uz6bnKJVAr93f+hb3dBFoAh3ICDRS5oC+VZCaZe/y\nhFmmwEtTr/7OHMyzK5udpfQyu233dOvzGr47gSbQgYxAI2UO6IEmufau8H3e3PodyfrrjLUP\neDc9R/08+cZbfDq7kjYCTaADGYFGyhzQjwpx97e39RQTaNlLrwofPapem+c9fIe4k3KMS+Gu\n8+fg6SLQBDqQEWikzAGdIx44N9He1rkHG1sf6eCqD0dNvfTkvt+iO5sv93rLywl5FoEm0IGM\nQCNl8CqOFedW1ZrYfuLn7AMiBB6yUNFc7jfOYL8H7r2f5uT3nRmOQBPoQEagkTJ6o0reOgcb\n57w69jVVlzkvEw+IbgzeT11XAH2et5PyKAJNoAMZgUYK9J2EyoZ+2jzDPRvb/QSx9x3eTsqj\nCDSBDmQEGqliAj3OBPoLbPeZxutxm9q95yazEWgCHcgINFLFBNp8lmm9neD+nx5ftVa35Z5O\nybMINIEOZAQayU+gi9dbXianEOjQYAPo59HdfwuHVF1e4joCTaADGYFG8g/onBtraXWGyp+H\n5BboVa+9ly1dWfxsx0PO/hgem29UQSLQ6iPQSAQ6Rb2ML7H95Bu4A/qWLE2rO97NCBYRaCQC\nrT4CjUSgS/eN9cM2Qi6BnmAMXt27t1wlRaCRCLT6CDQSgS5d9IGh8sdqugL6GDF6LxdDWESg\nkQi0+gg0EoEu3fsm0J9It3AFdGMxekdzceddbVtdtsTFeMkRaCQCrT4CjUSgS7fzQEPQg+U3\nC7oCup0A+nKxVHiivlB7gXz7t/r3HmPxC8sSEWgkAq0+Ao1EoFM0s0HEzEayp9WFXAItzqDU\n+FosjUv+Pl263vrqlpvsjk6gkQi0+gg0EoFO1aZxQ5/carHe3VUco2ppWuPoc+97m8/3l113\nbZ4Qt/0aEwKNRKDVR6CRCDSSy+ugt3wyK3ajYB8BcE3ZtuKSP62B3bEJNBKBVh+BRiLQSB7e\nSfiiALirbH13sb6W3fEINBKBVh+BRiLQSB4CXXye7m/DlbL19wqgT7E7HoFGItDqI9BIBBrJ\ny2dxFD3d7bQh8ju/c1oZv1L8yu5wBBqJQKuPQCMRaCSVD0sq2fq+B9TrbHFFSYkINBKBVh+B\nRiLQSJkE2mEEGolAq49AIxFoJAINRaAJdCAj0EgEGolAIxFo9RFopLID9Kon7n6j0K+5lIhA\nQxFoAh3ICDRSMtAv1NI07Rj51Q4ZjUBDEWgCHcgINFIS0MtqGZcDX5CZQ28fdnrneyzeCkig\noQg0gQ5kBBopCej7xP0aVbbZ3Lnopb5DLJ4QZ922Q/VjHSkXutwC/XWX/Q69QdkrwQk0gQ5k\nBBopCegh5jOaV9nbd8W+kW0r9QWPfL041u3SDcor0F/V0P/cx8qfs+ouAk2gAxmBRkoCWrwn\nSqtfYGvXohZi82flm1gNdKTYu710gxJAFy2dvcPWvDKQK6BPFH/wMd5NJykCTaADGYFGSgI6\n9wgndHxpft8+WrI+f+QB2oH35sc/yHvmxpELY0utxd7HS8dPBvqLyPY1R9ibmfJcAZ0l/uCX\nejedpAg0gQ5kBBop+SqO77tW0fYeLXtqconeNIHeX7J+kLH22tjyupb6I5kfjS5eLfa+WTp+\nEtDrGhpbj7U3NdW5ArqOw4dPO4xAE+hARqCRSt6osnOVTZ5Dofkm0CelXr3MXL0s+oHxRDmt\n+nxzceMB+uIh8l9IJgF9txhsv4SP1k2ZusXuXD3OFdA9xB9lknfTSYpAE+hARqCR3NxJ2MGA\npvJnqde+bgIdfatJThWxfGd0g+xrjz3uJouLGZKANh+5r8XfGziiuqbVmwBP3lWugF5n/Jvp\nMu9mkxyBJtCBjEAjuQF6Q1v9G/HTkrUfmKR+EN3aXL7e7vBJQA81f38Z++Al8X18pvNpe5C7\ny+y23dPtP696NpeSEWgCHcgINJK7Z3GsmPih9MbwnH0NQvfNMZeLGgtjbX/pTQJ6YU1j5yGx\nD9qL0S5xPGcv4o0qSARafQQaqdwCbdmH+m/D6nwYW37OENX+9b/JV3G8VC+yc/f4zgcIoE/0\nYqaOI9BIBFp9BBqpYgIdWnNvv3vXJCw/c7BW87K1tncvcR109qTx8xIWzW/QPd1NEYxAIxFo\n9RFopAoKdOl2FDnY2PpOwkniHPQXLmeERaCRCLT6CDQSgU7Z5qdun7BdvjrNrd7319S0Bs97\nPCWbEWgkAq0+Ao1EoFM1U7/3ZD/5i1rTPYsj+4Ppdp/q5HUEGik4QP/6k6t2h392N4C6ftvl\n9wyk7Qr/4vcUZP2y2+8ZSPvL7f9Y4QoONE5StAzJNvj5n0xOx1F/hn/3ewrS9vg9AWl/hP9w\ntf8vngH9p7v2uB1AXX//4/cMpP0T/svvKcj6a4/fM5C2O/y31eo/Fr797e9qjjzdvC76K9kG\nf/2r5sAelOZvzdeC+7e2K7zL3QCeAc1THD7EUxxI1qc4VurXSrRZruTIL5pAT5ZtkMHHjRaM\nOePE69bZ356nOJCCc4qDQPsQgUayBLpYPBmzjZK3FH5tAi3lvyTQebM/UvQyrqLO+kQafG97\nBwKNRKDVR6CRyirQc0xDZ3h0sKKlXyZctXGxMXY/6dYlgP6wqaZlDbH9KCcnjRd/zK62dyDQ\nSARafQQaqawC/ZYJ9IveHOvLIzStxrAYsdsH1dBq3Zwr3TwZ6O/rGVMZ7c1UkrtM/DFr296B\nQCMRaPURaKSyCvQ8E+jo8+o+Pa1B8xu3oofaIB7O8VD8k8LVVjeuJAN9m5hKE3Nxx4izuoz2\n6q1Rl4qxa9negUAjEWj1EWiksgp0sXFuVjvJZFRcd9HB3guxSme+krah3e2Tge5t/stCvKFl\nm/7wf62dR0KPE0OfZXsHAo1EoNVHoJHKKtChdWdG3Dr9B3PJfEnVePBQ/U1i7d5dkgy0+bzR\nRmLpWrHk0SuwCk/WB9trWfotzQg0EoFWH4FGKrNAh0JL31sU/THXBHYAeKg7xO517D6PIxno\nJbWNve8WS4eLsU4Bp1KyvJEnHd13pf3tCTQSgVYfgUYqw0AnVFBVqHgdeCiT2Bvsbl/iKo43\nG+nXfJhX/LUUU/HnYaMEGotAq49AI5UPoEPnCBU/TL9l6ibtHdn7AvB50KHQ9qmTYtdMXy6m\nMhSdissINBKBVh+BRionQK9q4uYLdKRNr4//2v7WVncSrjNez9KcD0sqHYEm0IGMQCM5eprd\n1nt79H9f2VRKZnmr95r+hx953caMzaVEBBqJQKuPQCOVF6AzWwafxeE0Ao1EoNVHoJEINBKB\nhiLQBDqQEWik4AC98ppTu7+S+IEToHNHHN+q56L023kUgUYi0Ooj0EgEOn3za+m/9rsq4RMH\nQBedpu9cc77300odgUYi0Ooj0EgEOn1txIVz0+KfOAD6WbHzCQrmlTICjUSg1UegkQh02jab\ntyneEv/IAdB9xc5V0MeEOI1AIxFo9RFoJAKdtmwT6CHxjxwAPUDsXE3JmwVS5BToNcuVPMc6\nZQSaQAcyAo3kH9Czep/c58v44mHC2IQXYDkAepLY+QwPp2eZM6A/PVzTmrykbDIlItAEOpAR\naCTfgH7GIHVibHmGsXxBwhZOruLoru+8t5qXJ6bIEdDL9zL+aB+om05SBJpABzICjWQN9M6X\n7p6o5nbqjeLJSXU2xT756sJDOzyUn7CJE6CLJnQ7dfB676aXJkdADxRf7zuom05SBJpABzIC\nnbo1K6zWWgI9v2kEliZfeD0jvXfMc87vyDcpLzeqiLceaPuom05SBJpABzICnappLTXtgNfk\n662ALhRPXT5op4J5vWkC/Vbsk5k3X/lo0pHKC9CXiD9pK3XTSYpAE+hARqBTtEicSZC/ltsK\n6C9MRKcomNjaLGPorHXRD4bpi83WJmxSXoB+X/wt3q9uOkkRaAIdyAh0isznJp8u3cAK6HdN\noJ9XMbP7jaFHRRdnikOdF99g7iPPZOzOQKc5u4pjhP4vo8vsvkjGbQSaQAcyAp2iE4V7B0g3\nsAJ6mQn0HBUzC73eqXmnN2NLN4tDVY0+zr+4v744WMmR3efwOugl48Z8mX4rjyLQBDqQEegU\nnS/cO0a6wZKPvpJ/tetj7NzN/uHWT5sH3sxnXuoQe6Psk2LxZWw01fFOQiQCrT4CjeQf0Obv\n4sZIVq/rGFnZZqls75xBWVq1flvtHqxwUFVNa/m50zkaPSUmekh0uUOGbz1xFoFGItDqI9BI\nPl7FcZvO3OWyG43FFWBH50tWh0L5y2y/QjAUussYrfEGZzM0DyQelvRedPlQAfRxyFjqI9BI\nBFp9BBrJz+ugFz4+RnoOeYF5XmGqJ0cqqidGewDaO7t/w6y2MZ9DXcRYPT2ZmecRaCQCrT4C\njRTUOwnNC8C0CXZ3yJ9w7d3S175uNEcbiE4n8Xv+rOr6UDW/RcdSG4FGItDqI9BIQQX6O5PU\nj2xun91Kv3RZdkFvobjmWhvpydwmN9O0lh96MpT3EWgkAq0+Ao0UVKBDZxuitrF75UV3IbDs\nkrHBxtr6q+wNtrBL/b3PX5z4yZZZSU/l/GGHzWllPgKNRKDVR6CRAgv0hjMjop5g+bCOhArE\n3X+Jz2xOKu/SyMr93rc32Mq99aH2WR37oHBwZPi238S3KC93EmY4Ak2gAxmBRlo1Y6HtZ8lv\nN8+IXCXd4ruXp+bYHKy3GOvK2Ad3GsvN4hf1EWgoAk2gAxmBRnL0POiDBKqPe3Hg1iVuocmv\nXXJwAg1FoAl0ICPQSI6Afs0g9MhcLw7cTnh8YnT5B/PrefzubgINRaAJdCAj0EjO3qjy6mGV\navdcY3PjtX1btuwn3fge4fGD0eWd5gnu2OOTCDQWgSbQgYxAIzl95dVO22ess/fXvd0vW7I6\nX7/LXOscf83rFeIakPhvDUsAvWN1KDARaCQCrT4CjVSOgLbfwDS/USx6oV//lxO4365fUdIo\n4dnTSUAv7lRJa/yUgmlCEWgkAq0+Ao1UIYE+VgB9lP09vnz6rcQHMyUCvbWZMZiSJ1MDEWgk\nAq0+Ao1UfoDOl52xKN3xAug2jqcULRHoB8VgB8KDeRuBRiLQ6iPQSOUF6FXdqmn7PmFz4zuE\nqbdB09JLBPpK8xqPgNxcSKCRCLT6CDRSOQE670gDSZtngnONcxy1J4ITSwbafOFKzUy9NypN\nBBqJQKuPQCOVE6DHCyX3salk3lnG5veCM0sC+ivj4XZaX3QsjyPQSARafQQaqZwAPdg8z7BW\nsr5oxZbExVVVja2ryTZPV9JVHGN1oU/YDg7ldQQaiUCrj0AjlROgRwifq0getzFmb03r+F18\n+TXT87fBqSVfB71s7PB3bV+DrToCjUSg1UegkcoJ0AtrGOBekHqtOAHSLP4lerIJ9JTU26eN\ndxJCEWgCHcgINJKjqzie1s8zHCG50m6/krdqb6prfFDP9ktnS0SgoQg0gQ5kBBrJ2XXQyx6+\n7VXJ0/13mN+X+8U/ekFfznoVnRqBhiLQBDqQEWgkV3cSzn7w/i+iPxfVFEAnPs3/6wFnXjUf\nHv2/P3725U58cioj0EgEWn0EGqmsAD1r8GX3bba/r/G0jcujv7nrJ4A+1bPf5D1eT9MaveLV\naJ5GoJEItPoINFIZAdq4n7rhIru7PidEjj5hf3sdsTzJo5m9Y4xWXfYCRF8j0EgEWn0EGqls\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WgoAk2gA1kZBfoyYWxTZNzoV+CnpFts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\nAGLq/wHDStL7ut7gLwAAAABJRU5ErkJggg=="},"metadata":{"image/png":{"width":720,"height":480}}}],"source":["#plot fitted against the observed data\n","ggplot(dat, aes(fitted, y_obs)) +\n"," stat_summary(geom='point',fun=mean)"]},{"cell_type":"markdown","metadata":{"id":"222zspi80ZAk"},"source":["Given your fitted model, you can also easily generate predictions of y given new values of x using the `predict` function:"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":34},"executionInfo":{"elapsed":149,"status":"ok","timestamp":1706697396830,"user":{"displayName":"Timothy Verstynen","userId":"04724296371017749786"},"user_tz":300},"id":"2ajyC3eS0ZAk","outputId":"fde77546-6e31-4cf0-ec64-e6625c466235","scrolled":false},"outputs":[{"output_type":"display_data","data":{"text/html":["1: 0.745373708644577"],"text/markdown":"**1:** 0.745373708644577","text/latex":"\\textbf{1:} 0.745373708644577","text/plain":[" 1 \n","0.7453737 "]},"metadata":{}}],"source":["new_data <- data.frame(x1=-5, x2=10) #new x-values to give to the model\n","predict(model_fit, newdata = new_data) #predict the y value for a given x"]},{"cell_type":"markdown","metadata":{"id":"bgYKszfvEyRj"},"source":["That's all for now! We'll dive into some more advanced functions for data manipulation in R in the next tutorial."]},{"cell_type":"markdown","metadata":{"id":"BUm4wLV1ibtZ"},"source":["*Notebook authored by Ven Popov and edited by Krista Bond, Charles Wu, Patience Stevens, Amy Sentis, and Fiona Horner.*"]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"R","language":"R","name":"ir"},"language_info":{"codemirror_mode":"r","file_extension":".r","mimetype":"text/x-r-source","name":"R","pygments_lexer":"r","version":"4.2.0"}},"nbformat":4,"nbformat_minor":0}