13.6 Predicting with a Regression Equation

We predict that statistics students who earn a grade of 73 on the third exam will earn a grade of 179.08 on the final exam, on average.

a. What would you predict the final exam score to be for a student who scored a 66 on the third exam?

We predict that statistics students who earn a grade of 73 on the third exam will earn a grade of 179.08 on the final exam, on average.

b. What would you predict the final exam score to be for a student who scored a 90 on the third exam?

True or False? If False, correct it: Suppose you are performing a simple linear regression of Y on X and you test the hypothesis that the slope β is zero against a two-sided alternative. You have $n = 25$ observations and your computed test (t) statistic is 2.6. Then your P-value is given by .01 < P < .02, which gives borderline significance (i.e. you would reject $H_{0}$ at $\alpha = .02$ but fail to reject $H_{0}$ at $\alpha = .01$).

An economist is interested in the possible influence of "Miracle Wheat" on the average yield of wheat in a district. To do so they fit a linear regression of average yield per year against year after introduction of "Miracle Wheat" for a ten year period.

The fitted trend line is

$\overset{^}{y}_{j} = 80 + 1.5 \cdot X_{j}$

($Y_{j}$: Average yield in j year after introduction)

($X_{j}$: j year after introduction).

1. What is the estimated average yield for…

An interpretation of $r = 0.5$ is that the following part of the Y-variation is associated with which variation in X:

1. most
2. half
3. very little
4. one quarter
5. none of these

Which of the following values of r indicates the most accurate prediction of one variable from another?

1. $r = 1.18$
2. $r = −.77$
3. $r = .68$