# The regression equation for predicting grade point average from

```1. The regression equation for predicting grade point average from number of hours studied
is determined to be GPA = 1.95 + 0.05(Hours). Interpret the slope of the regression line.
Answer: For each additional hour studied, the GPA is predicted to increase by 0.05
points.
2. Which of the following is not a necessary condition for doing inference for the slope of a
regression line?
a. For each given value of the independent variable, the response variable is
normally distributed.
b. The values of the predictor and response variables are independent.
c. For each given value of the independent variable, the distribution of the response
variable has the same standard deviation.
d. The mean response values lie on a line.
Answer: (b) is not a condition for doing inference for the slope of a regression line. In
fact, we are trying to find out the degree to which they are not independent.
3. True–False: Significance tests for the slope of a regression line are always based on the
hypothesis H0: β = 0 versus the alternative HA: β ≠ 0.
Answer: False. While the stated null and alternative may be the usual hypotheses in a test
about the slope of the regression line, it is possible to test that the slope has some
particular non-zero value so that the alternative can be one sided (HA: B &gt; 0 or HA: β &lt; 0).
Note that most computer programs will test only the two-sided alternative by default. The
TI-83/84 will test either a one- or two-sided alternative.
4–10. The following table gives the ages in months of a sample of children and their mean height
(in inches) at that age.
4. Find the correlation coefficient and the least-squares regression line for predicting height (in
inches) from age (in months).
r = 0.9817, height = 25.41 + 0.261(age)
5. Draw a scatterplot of the data and the LSRL on the plot. Does the line appear to be a good
model for the data?
The line does appear to be a good model for the data.
6. Construct a residual plot for the data. Does the line still appear to be a good model for the
data?
The residual pattern seems quite random. A line still appears
to be a good model for the data.
7. Use your LSRL to predict the height of a child of 35 months. How confident should you be
in this prediction?
Height = 25.41 + 0.261(35) = 34.545 (Y1(35) = 34.54). You probably shouldn't be too confident in this
prediction. 35 is well outside of the data on which the LSRL was constructed and, even though the
line appears to be a good fit for the data, there is no reason to believe that a linear pattern is going
to continue indefinitely.
8. Interpret the slope of the regression line found in question #1 in the context of the problem.
The slope of the regression line is 0.261. This means that, for an increase in age of 1 month,
height is predicted to increase by 0.261 inches. You could also say, that, for an increase in
age of 1 month, height will increase on average by 0.261 inches.
9. The national institute of pediatrics believes that age does impact the height of children.
Based off this claim, does the data illustrate a correlation? (complete all the steps)
Assumptions: Observations are independent, relationship is linear as seen above, standard
deviation is constant, and responses vary normally
Ho: β = 0
Ha: β ≠ 0
Calculations: t = 15.487, p = 8.547 x 10−8
Interpretation: Since p &lt; α, I reject the null hypothesis. There is sufficient evidence that age
can predict height in children.
10. Perform a 95% confidence interval for the true mean slope of the LSRL of this data.
We are 95% confident that the true slope of the LSRL of height and age is between 0.223 and
0.299.
```