Chapter 3.2, Problem 38E

(a)

To determine

To find: The slope of the line

Answer to Problem 38E

The slope is b = 0.882

Explanation of Solution

Given:

Predicted reading score = $-33.4+0.882$ (IQ score)

Calculation:

On comparing our equation to general equation of regression we get, the slope is: b = 0.882

This tells us that the reading score is predicted to go up by $0.882$ for each added IQ score.

Conclusion:

Hence, the slope is: $b=\mathrm{0.882.}$

(b)

To determine

To find: The intercept and explain why the intercept value is not statistically meaningful.

Answer to Problem 38E

The intercept is: a = -33.4

The value of the Y intercept is meaningful only when the explanatory variable can actually take values close to zero.

Explanation of Solution

Calculation:

On comparing our equation to general equation of regression we get, the intercept is: a = -33.4

The value of the Y intercept is meaningful only when the explanatory variable can actually take values close to zero.

Conclusion:

Hence, the intercept is: a = -33.4

(c)

To determine

To predict: reading scores for two children.

Answer to Problem 38E

The reading score is 81.26 with IQ score 130 and it is 45.98 with IQ score 90

Explanation of Solution

Calculation:

The regression line is:

(Predicted) reading score $=-33.4+0.882$ (IQ score)

When IQ score = 90 then

(Predicted) reading score $=-33.4+0.882\left(90\right)=45.98$

Reading score will be 45.98 with IQ score 90.

When IQ score = 130 then

(Predicted) reading score $=-33.4+0.882\left(130\right)=81.26$

Conclusion:

Hence, the reading score is 81.26 with IQ score 130 and it is 45.98 with IQ score 90