Question

1. The director of admissions at a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year can be predicted from their ACT test score. The data can be found at "GPA.txt". (a) Fit a simple linear regression using ACT score as the explanatory variable, and GPA as the response variable by computing ?X, ?Y and then SXX, SXY and SYY. Use the values of ?X, ?Y, SXX, SXY and SYY from (a) to answer the following parts. (b) Estimate the parameter ?. (c) Use a t-test to determine whether or not there a linear relationship between ACT score and GPA. (d) Compute the ANOVA table corresponding to the model. (e) From the table determine the mean square error (MSE). (f) Use the ANOVA F-test to determine whether or not there is a linear relationship between ACT score and GPA. (g) How do the results in (e) compare to those in (b)? (h) How do the results in (f) compare to those in (c)? (i) What proportion of the variation in GPA is explained by the regression model?

          1. The director of admissions at a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year can be predicted from their ACT test score. The data can be found at "GPA.txt".

(a) Fit a simple linear regression using ACT score as the explanatory variable, and GPA as the response variable by computing ?X, ?Y and then SXX, SXY and SYY.

Use the values of ?X, ?Y, SXX, SXY and SYY from (a) to answer the following parts.

(b) Estimate the parameter ?.
(c) Use a t-test to determine whether or not there a linear relationship between ACT score and GPA.
(d) Compute the ANOVA table corresponding to the model.
(e) From the table determine the mean square error (MSE).
(f) Use the ANOVA F-test to determine whether or not there is a linear relationship between ACT score and GPA.
(g) How do the results in (e) compare to those in (b)?
(h) How do the results in (f) compare to those in (c)?
(i) What proportion of the variation in GPA is explained by the regression model?

1. The director of admissions at a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year can be predicted from their ACT test score. The data can be found at "GPA.txt".

(a) Fit a simple linear regression using ACT score as the explanatory variable, and GPA as the response variable by computing ?X, ?Y and then SXX, SXY and SYY.

Use the values of ?X, ?Y, SXX, SXY and SYY from (a) to answer the following parts.

(b) Estimate the parameter ?.
(c) Use a t-test to determine whether or not there a linear relationship between ACT score and GPA.
(d) Compute the ANOVA table corresponding to the model.
(e) From the table determine the mean square error (MSE).
(f) Use the ANOVA F-test to determine whether or not there is a linear relationship between ACT score and GPA.
(g) How do the results in (e) compare to those in (b)?
(h) How do the results in (f) compare to those in (c)?
(i) What proportion of the variation in GPA is explained by the regression model?

Added by Patricia P.

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