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# UC Davis - STA 108 Applied Statistical Methods: Regression Analysis - Sample - Q2 Linear Regression Model

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2. Data were collected at a large university on n = 224 computer science majors in a certain year. The purpose was to predict the cumulative GPA after three semesters in college. Among the predictors were high school grades in mathematics (HSM), science (HSS), and English (HSE). The follow multiple linear regression model was considered:

Y = b0 + b1x1 + b2x2 + b3x3 + e                             (1)

where x1 = HSM, x2 = HSS, and x3 = HSE.

(a) What does   stand for in (1)? and what are the assumptions for e?

(b) Partial results for the estimated regression coefficients for (1) are:

b0 = 0:590, b1 = 0:169, and b3 = 0:045. (Note result for b2 is not here.)

The corresponding standard errors are 0:294, 0:035, and 0:039, respectively. Which of the above regression coefficients is(are) NOT significant at 5% level? Please justify your

(Note: a regression coefficient,  bj , is significant at 5% level if the null hypothesis H0 :  j = 0 vs H1 :  j 6= 0 is rejected at the level   = 0:05. Also, because the sample size, n, is fairly large, normal table can be used instead of the t-table.)

(c) The following is a partial ANOVA table for fitting model (1):

Source                           SS        d.f.        MS                   F

Regression                                             9.237

Error                             107.750

Total

In addition, another regression model was considered by dropping HSS from model (1), that is,

Y = b0 + b1x1 + b3x3 + e                 (2)

The corresponding partial ANOVA table is given below:

Source                           SS        d.f.        MS                   F

Regression                     27.303

Error

Total

Based on the information, do you think dropping HSS from (1) is a right decision? Test using   = 0:05.

(Note: You do not have to complete the entire ANOVA tables in order to answer the question; you just have to get the relevant parts.)

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