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Posts: 203
3 weeks ago
A college admissions counselor was interested in finding out how well high school grade point averages (HS GPA) predict first-year college GPAs (FY GPA). A random sample of data from first-year students was reviewed to obtain high school and first-year college GPAs. The data are shown below:




Is there evidence of an association between high school and first-year college GPAs? Test an appropriate hypothesis and state your conclusion in the proper context.
Textbook 

Stats: Modeling the World


Edition: 4th
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Posts: 266
3 weeks ago
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We have high school and first-year college GPAs for a random sample of first-year college students. We want to know if there is an association between high school and first-year college GPAs.
H0: There is no association between high school and first-year college GPAs. β1 = 0
HA: There is an association between high school and first-year college GPAs. β1 ≠ 0
*Straight enough: There is no obvious bend in the original scatterplot of the data or in the plot of residuals against predicted values.
*Independence: These data were not collected over time, and there is no pattern in the residuals.
*Does the plot thicken?: Neither the original scatterplot nor the residuals plot shows any disturbing changes in the spread about the line.
*Nearly Normal: A histogram of the residuals does not deviate too much from being unimodal and symmetric.
Under these conditions the regression model is appropriate. We will use a linear regression t-test.

Regression equation: FY PA = -1.5641 + 1.3053(HS GPA)

The R2 for the regression is 75.4%. High school GPA seems to account for just over 75% of the variation in first-year college GPA. The regression equation indicates that each additional tenth of a point in high school GPA corresponds to an increase in first-year college GPA by an average of about 0.13 points.

With a very small P-value ≤ 0.0001, we reject the null hypothesis. There is strong evidence of an association between high school and first-year college GPAs.
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