Question:
06.21 Table 6-15 gives data on verbal and math S.A.T. scores for both males and females for the period 1967-1990.
http://public.sheet.zoho.com/public/btzoho/table6-15
a. You want to predict the male math score (Y) on the basis of male verbal score (X). Develop a suitable linear regression model and estimate its parameters.
b. Interpret your regression results.
c. Reverse the roles of Y and X and regress the verbal score on the math score. Interpret this regression.
d. Let a2 be the slope coefficient in the regression of math score on the verbal score score and let b2 be the slope coefficient of the verbal score on the math score. Multiply these two values. Compare the resulting value with the r² obtained from the regression of math score on verbal score or the r² value obtained from the regression of verbal score on math score. What conclusion can you draw from this exercise?

[my adds]

I used Excel’s regression add-in to produce the ANOVA table below; I regressed Male Math scores (explained) on Male Verbal scores (explanatory). The OLS regression equation produced is: MATHM = 262.8 + 0.5386 * VERBM. Here is the ANOVA table produced by Excel:

• e. How many estimators are there in this two-variable (univariate) regression?
• f. What distribution characterizes all three estimators, including d.f., and why?
• g. Show how the 95% confidence interval for each coefficient (slope and intercept) is calculated.
• h. Test your hypothesis that the true slope (i.e., of the PRF function) is 0.5.
• i. What is the standard error of regression (SER) and what does it mean?
• j. The coefficient of determination is given as 0.8842. Confirm this by using the ANOVA table to calculate the R^2.
• k. What does the F value signify?

Answers here in forum or here in wiki.

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