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1. ANOVA Table. Download the "GFCLOCKS. RData" to your lap- top, and refer to "Lecture.R" script to load the R Workspace. See R code below load("GFCLOCKS RData' ')###load the R Workspace "CFCLOCKS.RData' 1s()###View objects names (GFCLOCKS)###Display all variable names in GFCLOCKS dataset GFCLOCKS[1 5,] attach(GFCLOCKS) par(mfrow=c( 2)) plot (PRICE AGE) plot (PRICE"NUMBIDS) (a) Build multiple linear regression model that predicts PRICE us- ing both NUMBIDS and AGE. Show also the estimated regression coefficients using output. (b) What is the fitted regression model? (c) Refer to lecture slides for lecture 5. use R function anova() to produce the ANOVA table. Show your ANOVA table. (d) We know that MSE SSE/error degrees of freedom. From the ANOVA table, MSE and error degress of freedom are 17818 and 29. respectively. What is SSE? (e) From the ANOVA table, SSR 2555224 1727838 4283062 What then SST? (f) What is the F statistic? Show R output. (g) The null and alternative hypotheses of the global F test is Hn PNUMBIDS PAGE 0;Ha At least one of them is not equal to 0 If Ho is true, what is the distribution of the F statistic (test statistic)? (h) At o = 0.05 level of significance, do we have sufficient evidence to show that at least one of the predictors is statistically significant` Show your reasons (please use appropriate statistical language) 3. (Dummy Variables)To predict performance on the GRE graduate entrance exam (response Y GRE score), undergraduate college stu- dents were asked to follow of study programs. In addition, another variable x High school GPA was also recorded. If we consider the third study program as the baseline, we can define the following two indicator variables to account for the categorical predictor "study pro- grams" f study program 1 1, study program 2 I1 I2 = 0, otherwise (o, otherwise The population model considered is E(Y) 38 8111 8212 BaX (a) Based on the model. write down the relationship between Y and x for students who followed program 1. (b) Based on the model. write down the relationship between Y and x for students who followed program 2. (c) Based on the model. write down the relationship between Y and x for students who followed program 3. (d) Give an appropriate interpretation for in (e) Which one of the following statements is NOT true? ( ) i. SA is the difference in slopes when regressing GRE score on High School GPA between students in study program and students in study program 3. 2 ii. Both I1 and I2 are dummy variables iii. There are three dummy variables created for modeling Y. iv. "Study program" is categorical predictor variable.

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1. (a) Build a multiple linear regression model that predicts PRICE using both NUMBIDS and AGE. Show also the estimated regression coefficients using R output.

Solution:
Multiple Linear regression model predicting PRICE by using NUMBIDS and AGE can be built using the following equation:
PRICE = beta0 + beta1*NUMBIDS + beta2*AGE
Where, beta0 is the intercept term, beta1 and beta2 are the coefficients of NUMBIDS and AGE respectively.

R Code:
fitted.lm <- lm(PRICE~AGE+NUMBIDS)
Coefficients from the R output:
(Intercept)         AGE    NUMBIDS
-1338.95134    12.74057    85.95298

1. (b) What is the fitted regression model
Solution:
We have Intercept term i.e. -1338.95134, coefficient of AGE and NUMBIDS are 12.74057 and 85.95298 respectively. Using intercept and coefficient final fitted mode is:
PRICE = -13338.95 + 12.74 * AGE + 85.95 * NUMBIDS...

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