Question

USING R STUDIO- Write the r commands for the following.

1. Non-Linear Models

1.1 Load the {ISLR} and {GGally} libraries. Load and attach the College{ISLR} data set.

[For you only]: Open the College data set and its help file and familiarize yourself with the data set and its fields.

1.2 Inspect the data with the ggpairs(){GGally} function, but do not run the ggpairs plots on all variables because it will take a very long time. Only include these variables in your ggpairs plot: “Outstate”,“S.F.Ratio”,“Private”,“PhD”,“Grad.Rate”.

1.3 Briefly answer: if we are interested in predicting out of state tuition (Outstate), can you tell from the plots if any of the other variables have a curvilinear relationship with Outstate? Briefly explain.

1.4 Regardless of your answer, plot Outstate (Y axis) against S.F.Ratio (X axis). Then, please answer, do you now see a more curvilinear pattern in the relationship?

1.5 Fit a linear model to predict Outstate as a function of the other 4 predictors in your ggpairs plot. Store your model results in an object named fit.linear. Display a summary of your results.

1.6 Briefly answer: Does this seem like a good model fit? Why or why not?

1.7 Now add an interaction term for S.F.Ratio with Private. Store your model results in an object named fit.inter. Display a summary of your results. Then do an anova() test to evaluate if fit.inter has more predictive power than fit.linear.

1.8 Briefly interpret the coefficients of the interaction term and the ANOVA results

1.9 Now use the poly() function to fit a polynomial of degree 4 for S.F.Ratio. Store your model results in an object named fit.poly. Display the summary results. Then conduct an anova() test to evaluate if fit.poly has more predictive power than fit.linear.

1.10 Briefly interpret your results.

Answer 1

1.3 S.F. Ratio has a curvilinear relationship with Outstate as seen from plot

> install.packages("ISLR") > library(ISLR) > install.packages("GGally") package ‘progress’ successfully unpacked and MD5 sums checked package ‘reshape’ successfully unpacked and MD5 sums checked package ‘GGally’ successfully unpacked and MD5 sums checked The downloaded binary packages are in         C:\Users\H311857\AppData\Local\Temp\RtmpOiMLSp\downloaded_packages > library(GGally) Loading required package: ggplot2 > view(College) Error in view(College) : could not find function "view" > attach(College) > View(College) > dim(College) [1] 777 18 > head(College)                              Private Apps Accept Enroll Top10perc Top25perc F.Undergrad Abilene Christian University     Yes 1660   1232    721        23        52        2885 Adelphi University               Yes 2186   1924    512        16        29        2683 Adrian College                   Yes 1428   1097    336        22        50        1036 Agnes Scott College              Yes 417    349    137        60        89         510 Alaska Pacific University        Yes 193    146     55        16        44         249 Albertson College                Yes 587    479    158        38        62         678                              P.Undergrad Outstate Room.Board Books Personal PhD Terminal Abilene Christian University         537     7440       3300   450     2200 70       78 Adelphi University                  1227    12280       6450   750     1500 29       30 Adrian College                        99    11250       3750   400     1165 53       66 Agnes Scott College                   63    12960       5450   450      875 92       97 Alaska Pacific University            869     7560       4120   800     1500 76       72 Albertson College                     41    13500       3335   500      675 67       73                              S.F.Ratio perc.alumni Expend Grad.Rate Abilene Christian University      18.1          12   7041        60 Adelphi University                12.2          16 10527        56 Adrian College                    12.9          30   8735        54 Agnes Scott College                7.7          37 19016        59 Alaska Pacific University         11.9           2 10922        15 Albertson College                  9.4          11   9727        55 > str(College) 'data.frame': 777 obs. of 18 variables: $ Private    : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 2 2 2 2 2 ... $ Apps       : num 1660 2186 1428 417 193 ... $ Accept     : num 1232 1924 1097 349 146 ... $ Enroll     : num 721 512 336 137 55 158 103 489 227 172 ... $ Top10perc : num 23 16 22 60 16 38 17 37 30 21 ... $ Top25perc : num 52 29 50 89 44 62 45 68 63 44 ... $ F.Undergrad: num 2885 2683 1036 510 249 ... $ P.Undergrad: num 537 1227 99 63 869 ... $ Outstate   : num 7440 12280 11250 12960 7560 ... $ Room.Board : num 3300 6450 3750 5450 4120 ... $ Books      : num 450 750 400 450 800 500 500 450 300 660 ... $ Personal   : num 2200 1500 1165 875 1500 ... $ PhD        : num 70 29 53 92 76 67 90 89 79 40 ... $ Terminal   : num 78 30 66 97 72 73 93 100 84 41 ... $ S.F.Ratio : num 18.1 12.2 12.9 7.7 11.9 9.4 11.5 13.7 11.3 11.5 ... $ perc.alumni: num 12 16 30 37 2 11 26 37 23 15 ... $ Expend     : num 7041 10527 8735 19016 10922 ... $ Grad.Rate : num 60 56 54 59 15 55 63 73 80 52 ... > ggdf <- College[, c(1,9,13,15,18)] > head(ggdf)                              Private Outstate PhD S.F.Ratio Grad.Rate Abilene Christian University     Yes     7440 70      18.1        60 Adelphi University               Yes    12280 29      12.2        56 Adrian College                   Yes    11250 53      12.9        54 Agnes Scott College              Yes    12960 92       7.7        59 Alaska Pacific University        Yes     7560 76      11.9        15 Albertson College                Yes    13500 67       9.4        55 > ggpairs(ggdf, ggplot2::aes(colour=Private)) plot: [2,1] [===============>---------------------------------------------------] 24% est: 3s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`. plot: [3,1] [============================>--------------------------------------] 44% est: 2s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`. plot: [4,1] [==========================================>------------------------] 64% est: 1s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`. plot: [5,1] [=======================================================>-----------] 84% est: 1s `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.                                                                                                > plot(College$S.F.Ratio, College$Outstate, type="b")

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