# Mathematics

HWK #5

1) For the companying data set,

X 2 6 6 7 9

Y 3 2 6 9 5

(a) I Have done it

(b) By hand, compute the correction coefficient. The correlation coefficient is r= (……). (Rounds to three decimal places as needed)

(c) Determine whether there is a linear relation between x and y. Explain.

(d) Find the critical value correlation for the sample size n= 5. Used the table of critical value for correlation coefficient. Explain.

2) An engineer wanted to determine how the weight of a car affects gas mileages. The following data represent the weight of various cars and their gas mileage.

Car weight pound miles per gallon

A 3590 18

B 2690 26

C 3180 23

D 3565 20

E 3680 19

(a) I have done it

(b) I’ve done it

(c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. r = (…….) (Round to three decimal places as needed)

(d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon based on the scatter diagram and the linear correlation coefficient.

3) Researcher wondered whether the size of a person’s brain was to related to the individual’s mental capacity. The selected 3 females and 3 males measured their MRI counts IQ scores. The data is below.

Females Males

MRI IQ MRI IQ

857,781 135 924,060 138

991,305 138 965,355 132

856,473 141 1,038,438 138

Treat the MRI as the explanatory variable. Compute the linear correlation coefficient between MRI count and IQ for both the males and the females. Do you believe that MRI count and IQ are linearly related?

A-the linear correlation coefficient for females is (…….)

B- the linear correlation coefficient for males is (…….)

(Rounds both to three decimal places as needed)

-Do you believe that MRI count and IQ are linearly related?

4) For the set below,

(a) Determine the list-squares regression line

(b) Graph the least-squares regression line on the scatter diagram.

X 3 4 5 6 8

Y 4 5 6 9 13

(a) Determine the list-squares regression line. Ŷ= (……) X + (…….)(Round to four decimal places as needed.

(b) Graph the least-squares regression line on the scatter diagram.

5)A pediatrician want to determine the relation that exists between a child’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences and obtains the accompanying data. Complete parts (a) through (g).

Data table. In inches

Height, x Head Circumference, y Height, x Head Circumference, y

27.75 17.7 27 17.3

24.7 17.1 27.5 17.5

25.5 17.1 26.75 17.3

25.5 17.3 26.75 17.5

25 16.9 27.5 17.5

27.75 17.6

(a) Find the least -squares regression line treating height as the explanatory variable and head circumference as the response variable.

The least squares regression line is Ŷ= (……) X + (……)(Round to four decimal places as needed)

(b) Interpret the slope and y-intercept, if appropriate.

(c) Use the regression equation to predict the head circumference of the child who is 25 inches tall.

(d) Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of child above average or below average?

(Residual=observed y – predicted y = y- Ŷ

(e) Draw the least squares regression line on the scatter diagram of the data and label the residual from part (d).

(f) Notice that two children are 27 inches tall. One has a head circumference 17.7 inch and other has a head circumference 17.3 inch. How can this be?

(g) Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 34 inches tall?

6) An engineer wants to determine how the weight of a car, x, affects gas mileages, y. The following data represent the weight of various cars and their miles per gallon.

Car A B C D E

Weight pounds, x 2660 2910 3290 3860 4015

Miles per Gallon,y 22.2 22.9 21.8 15.9 14.1

(a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Write equation for the least-squares regression line.

Ŷ= (…..) x + (…….)(Round to four decimal places as needed).

(b) Interpret the slop and intercept, if appropriate.

(c) Predict the miles per gallon of car B and compute the residual. Is the miles per gallon of this car above average or below average for cars of this weights?

(d) Draw the least squares regression line on the scatter diagram of the data and label the residual.