IQ and reading scoresData on the IQ test scores and reading test scores for a group of fifth-grade children give the following regression line: predicted reading score $-33.4+0.882$(IQ score).

(a) What’s the slope of this line? Interpret this value in context.

(b) What’s the intercept? Explain why the value of the intercept is not statistically meaningful.

(c) Find the predicted reading scores for two children with IQ scores of $90$and $130$, respectively.

It is given in the question that, the predicted reading score = $-33.4+0.882$(IQ score)

What’s the slope of this line? Interpret this value in context.

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

Here, the IQ score is the explanatory variable so $0.882$is the slope.

The slope of a linear regression line is the number multiplied by the explanatory variable.

The slope represents the predicted change in y when x increases by $1$unit.

It is given in the question that, the predicted reading score = $-33.4+0.882$(IQ score)

What’s the intercept? Explain why the value of the intercept is not statistically meaningful

For a value to be statistically meaningful it must lie in the realm of reality. Since the intercept is $-33.4$, that means a child with an IQ score of $0$would have a predicted reading score of $-33.4$which is out of the realm of possibility.

The y-intercept is the value of the response variable when the explanatory variable is $0$.

It is given in the question that, the predicted reading score = $-33.4+0.882$(IQ score)

Find the predicted reading scores for two children with IQ scores of $90$and$130$, respectively.

Given:

Reading Score = $-33.4+0.882$(IQ score)

We need to predict the reading scores corresponding to an IQ score of $90$and an IQ score of $130$.

IQ Score of 90

$\text{Replace "IQ score" with}90\text{in the given regression line and evaluate:}$

$\text{Reading Score}=-33.4+0.882\left(\text{Time}\right)$

Substitute

$=-33.4+0.882\left(90\right)$

Evaluate product

$-33.4+79.38$

Evaluate sum

=$45.98$

Thus the predicted reading score for a child with an IQ of $90$is$45.98$

IQ Score of 130

Replace "IQ score" with $130$in the given regression line and evaluate :

Reading Score = $-33.4+0.882\left(Time\right)$

Substitute

= $-33.4+0.882\left(130\right)$

Evaluate product

= $-33.4+114.66$

Evaluate sum

=$81.26$

Thus, the predicted reading score for a child with IQ of $130$is $81.26$