Simple Linear Regression Practice
1. Match each correlation with its possible scatterplot. Note all scatterplots will not be used.
A
C
B
D
E
___A___ 0
___C___ -0.44
___D___ 0.44
___B___ 0.85
2. The director of admissions of 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 score. The data collected from the
study can be found in the file GPA.jmp on the course website.
a. Create a scatter plot of the data. Is linear regression appropriate? Explain.
It appears that linear regression might be appropriate. There is a slight linear
trend emerging from the data.
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b. Determine whether the overall regression is useful. Be sure to include your hypotheses,
test statistic, p-value, and conclusion.
H0: The regression model is NOT useful
Ha: The regression model IS useful
F = 9.2402
p-value = 0.0029
Yes, there is evidence that regression is appropriate.
c. Using JMP find and interpret the coefficient of determination (R2).
R2 = 0.07
7% of the variation in GPA is explained by ACT score.
d. Using JMP, find the root mean square error (RMSE).
RMSE = 0.623 (from above output)
e. Using JMP, find the estimated regression equation. Give the equation below making
sure to use the appropriate statistical notation.
Ê(GPA | ACT) = 2.11 + 0.04* ACT
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f.
Interpret the intercept in context for the regression equation found in part e.
When ACT = 0, the best guess for a student’s college GPA is 2.11
g. Interpret the slope in context for the regression equation found in part e.
For every 1 point increase in ACT score, a student’s GPA will increase by 0.04
points.
h. Using the regression equation found in part e, find the predicted GPA for a student who
earned an ACT score of 23.
Ê(GPA | ACT) = 2.11 + 0.04(23) = 3.03
i.
Check the assumptions (linearity, constant variance, independence, normality, and
outliers) behind the regression analysis to make sure they are valid. Be sure to fully
explain why each assumption has (has not) been met.

Linearity – There does not seem to be any trends in the plot, and a
horizontal band is present. Thus, the assumption of linearity is OK.

Constant Variance – There does not seem to be an obvious pattern in the
data, and a horizontal band is present. Thus, the assumption of constant
variance in OK.

Independence – There is not any sequential pattern in the data. Thus, the
assumption of independence is OK.
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
Normality – The points seem to follow the reference line and the
histogram is somewhat bell-shaped (though it is slightly skewed left).
Thus, the assumption of normality is OK.

Potential Outliers – There appears to be 2 potential outliers indicated in
the plot above since they are outside the band of ± 1.25 (2(RMSE) = 1.25)
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