This problem is answered using the R code provided.

The data set is from the first year that SAT scores were published on a state-by-state basis in the U.S. It was originally published in the Harvard Educational Review in 1984, and is also reported in Ramsey and Schafer, 1997.

The variables included are:

sat = average total SAT score for the state

takers = percent of eligible students in the state who took the exam

income = the median family income of students in the state who took the exam

years = the average number of years that the test-takers had for studies in the core subjects

public = percentage of test takers attending public secondary schools

expend = the states expenditures on education in hundreds of dollars per student

rank = the median percentile ranking of the test-takers in their high-school class

a)Test whether the other six variables as a group are statistically significant predictors of the states average SAT scores. (Report the p-value and your conclusion)

b)Check the assumptions, and state whether you feel comfortable trusting the results of the regression.

c)Report the p-value for the t test for takers and interpret the results at an ?=0.05 level.

d)What percentage of the variation in state average SAT score do the six variables explain?

R code output in png

R R 4.0.3 . / |Import Dataset * 81 MiB - List - > sat . reg=Lm(sat~takers+income+years+public+expend+rank) R - Global Environment - Q summary (sat . reg) Data Call: sat . reg List of 12 a Im(formula = sat ~ takers + income + years + public + expend + satdata 50 obs. of 8 variables rank) Residuals: Min 1Q Median 3Q Max -60 . 046 -6.768 0.972 13.947 46.332 Coefficients: Estimate Std. Error t value Pr(>Itl) (Intercept) -94. 659109 211.509584 -0.448 0. 656731 takers -0. 480080 0. 693711 -0. 692 0. 492628 Files Plots Packages Help Viewer income -0. 008195 0. 152358 -0. 054 0.957353 Zoom Z Export - C . years 22. 610082 6.314577 3.581 0. 000866 public -0. 464152 0.579104 -0.802 0. 427249 expend 2. 212005 0. 845972 2.615 0. 012263 Normal Q-Q Plot rank 8. 476217 2. 107807 4.021 0. 000230 (Intercept) O takers 40 Oo O income O O years * * * OO public expend rank * * * O OO resid (sat.reg) O Sample Quantiles Signif. codes: 0 ' ***' 0. 001 '**' 0.01 '*' 0.05 ' . ' 0.1 ' ' 1 O -60 -40 -20 0 -40 -20 O O Residual standard error: 26.34 on 43 degrees of freedom O Multiple R-squared: 0.8787, Adjusted R-squared: 0.8618 O F-statistic: 51.91 on 6 and 43 DF, p-value: plot(fitted(sat. reg), resid(sat. reg)); abline(h=0) 850 950 1050 -2 0 2 qqnorm(residesat . reg)) fitted(sat.reg) Theoretical Quantiles