Question

Drive my car

a. Explain what the value of $r^2$tells you about how well the least-squares line

fits the data.

b. The mean age of the students’ cars in the sample was $x̄=5$ years.

Find the mean mileage of the cars in the sample.

c. Interpret the value of $s$.

d. Would it be reasonable to use the least-squares line to predict a car’s mileage from its age for a Council High School teacher? Justify your answer.

Short answer

a. It tells us about the variation between variables is best explained by least square regression line.

b. Mean mileage is $105800$miles.

c. $s=22723$

d. We can't use least squares line to predict the mileage of cars of teachers.

Step-by-step solution

Given Information

It is given that

Importance of r2

From table, $r^2=77\%=0.77$

Hence, $77\%$of variation between variables is explained by least square regression line.

Mean Mileage

Lest square regression line is $\hat{y}=a+bx$

From table $a=-13832$

$b=14954$

Least square equation becomes

$\hat{y}=-13832+14954x$

Now, $(\overline{x},\overline{y})$lies on least square regression line, so mean mileage is obtained by replacing $x$by $\overline{x}$

hence, $\overline{y}=\hat{y}$

$=-13832+14954\overline{x}$

$=-13832+14954\left(8\right)$

$=105800$

hence, mean mileage is$105800$miles.

Value of s

From table, $s=22723$

Hence, error made when predicting the mileage using least square regression line is on average$22723$miles.

Reason to use Least Square Line

It is due to the fact that least square was determined using data of students.

It is not representative of teachers and we cannot it to predict the mileage of cars of teachers.