Question

Show your work, the formulas used, and the substitutions to answer the questions about the following data:

Can your high school GPA predict your college GPA? To try to answer this, the following data were collected:

High School GPA:      1.72     3.51     2.45     2.85     2.84     3.46     1.97            3.47

College GPA:             2.61     3.66     3.25     3.23     3.46     3.07     2.88            3.16

1. Create a scatter plot of the data
2. Find the equation of the regression line
3. Calculate the correlation coefficient.
4. Is there a significant correlation between HS GPA and College GPA? Use α=.05.
5. Calculate the coefficient of determination. What does this value say about the relationship between HS GPA and College GPA?
6. What would you expect the college GPA to be of a person with a HS GPA of 2.88?
7. Create a 90% prediction interval for the college GPA of a person whose HS GPA was 2.88.

Answer 1

Regression Calculation:

1.

2.

r = 0.8986

3.

Crtical r-value for n = 8 and = 0.05 is 0.707 < 0.8986 i.e r is significant.

4.

R² = 0.8986²

= 0.8075

i.e. High school GPA explains only 80.75% of the variation in College GPA

5.

6.

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