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Chapter 10: Q 36. (page 644)

Drive my car

a. Explain what the value of r2tells you about how well the least-squares line

fits the data.

b. The mean age of the students鈥� cars in the sample was x虅=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鈥檚 mileage from its age for a Council High School teacher? Justify your answer.

Short Answer

Expert verified

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

b. Mean mileage is 105800miles.

c. s=22723

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

Step by step solution

01

Given Information

It is given that

02

Importance of r2

From table, r2=77%=0.77

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

03

Mean Mileage

Lest square regression line is y^=a+bx

From table a=-13832

b=14954

Least square equation becomes

y^=-13832+14954x

Now, (x炉,y炉)lies on least square regression line, so mean mileage is obtained by replacing xby x炉

hence, y炉=y^

=-13832+14954x炉

=-13832+14954(8)

=105800

hence, mean mileage is105800miles.

04

Value of s

From table, s=22723

Hence, error made when predicting the mileage using least square regression line is on average22723miles.

05

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.

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