A professor investigated some of the factors that affect an individual student\'

Question

A professor investigated some of the factors that affect an individual student's final grade in his course. He proposed the multiple regression model y = ?0 + ?1x1 + ?2x2 + ?3x3 + e, where y is the final mark (out of 100), x1 is the number of lectures skipped, x2 is 1 for male and is 0 otherwise, and x3 is the mid-term test mark (out of 100). The professor recorded the data for 50 randomly selected students. The computer output is shown below.

1. Write the estimated regression model and explain the meaning of slope coefficients.

2. What is the Goodness- of- Fit? What does this statistic tell you?

3. Do these data provide enough evidence to conclude at the 5% significance level that the model is overall significant?

4. Do these data provide enough evidence to conclude at the 5% significance level that the final mark and the number of skipped lectures are related?

5. Do these data provide enough evidence at the 5% significance level to conclude that the final mark of male students are lower than of female students?

6. Do these data provide enough evidence at the 1% significance level to conclude that the final mark and the mid-term mark are positively related?

Dependent Variable: Y Method: Least Squares Date: 03/11/12 Time: 14:35 Sample: 1 50 Included observations: 49 Variable Coefficient Std. Error t-Statistic Prob 41.6 4.18 1.17 0.63 0.300916 2.337 2.518 1.035 4.846 Mean dependent var S.D. dependent var Akaike info criterion X2 X3 1.66 1.13 0.13 R-squared Adjusted R-squared S.E. of regression Sum squared resicd Log likelihood Durbin-Watson stat 3716 8688Schwarz criterion F-statistic 6.558 Prob(F-statistic)

Explanation / Answer

From the given data

1. The regression estimated model is
Y = 41.6 - 4.18X1 -1.17X2 + 0.63X3

Slope of X1 is -4.18 which is less than 0 then it is negative correlation between x1 and Y
i.e. As one lecturer skipped (X1) increase the marks will decrease 4.18 marks when all remaining variables are fixed

Slope of X2 is -1.17 which is less than 0 then it is negative correlation between X2 and Y
i.e. As X2 is 1(male) the marks decrease 1.17 marks

Slope X3 is 0.63 > 0 then it is positive correlation between X1 and Y
i.e. As Midterm (X3) marks increase 1 test mark the marks increase 0.63 marks

2. F = 6.558 Probability = 0.0000< alpha 0.05
Therefore, the regression equation is best fit to the given data

3. H0: the model is overall not significant
H1:the model is overall significant
Probability = 0.0000< alpha 0.05 so we reject H0
Thus we conclude that the model is overall significant

4. H0: the final mark and the number of skipped lectures are note related
H1: the final mark and the number of skipped lectures are related
P-value of skipped lecturer X1 = 0.0120 < alpha 0.05 so we reject H0
Thus we conclude that the final mark and the number of skipped lectures are related

5. H0: the final mark of male students are not lower than of female students
H1: the final mark of male students are lower than of female students
P-value of X2 = 0.0008 < alpha .05 so we reject H0
Thus we conclude that the final mark of male students are lower than of female students

6. H0: the final mark and the mid-term mark are not positively related
H1: the final mark and the mid-term mark are positively related
P-value of X3 is 0.0000 < alpha .01 so we reject H0
Thus we conclude that the final mark and the mid-term mark are positively related

Estiamte SE Coef. T P C 41.6 17.8 2.337078652 0.0196 X1 -4.18 1.66 -2.518072289 0.0120 X2 -1.17 1.13 3.36 0.0008 X3 0.63 0.13 9.79 0.0000

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