Here is the variables I got for question a) Fit a linear regression for writing on math [do not use any log transformations] and show the regression summary. [Hint: use the lm function to get the linear model and summary(lm object name) to get the model summary; make sure to name your saved object lm.out1]

Call: lm(formula = Writing ~ Math, data = SP.noNA) Residuals: Min 1Q Median 3Q Max -24.5965 -6.8672 -0.0488 7.0639 23.2251 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 13.42150 1.29780 10.34 <2e-16 Math 0.81802 0.01904 42.97 <2e-16 (Intercept) *** Math *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 9.244 on 994 degrees of freedom Multiple R-squared: 0.6501, Adjusted R-squared: 0.6497 F-statistic: 1847 on 1 and 994 DF, p-value: < 2.2e-16

Answer the following questions in R studio b) Write out the regression equation [round both parameter estimates to two decimal places]. No interpretations needed.

c) In the HW3 template, we provide code to create a scatterplot of writing on math. You need to complete the geom_abline(intercept=, slope=) part of the code, filling in the values for the estimated y-intercept and slope, to create a scatterplot that shows the regression line. Interpret the scatterplot. d) Interpret the estimated slope parameter for the regression line in the context of the problem. e) Interpret the coefficient of determination in the context of the problem. f) A student with a math score of 75 has a residual of 13.77, rounded to two decimal places. What was their observed writing score? Show your work