1. Given are five observations collected in a regression study on two variables.

xi	2	6	9	13	20
yi	7	19	8	27	23

Develop the estimated regression equation for these data.

=

Use the estimated regression equation to predict the value ofywhen

x=13.

2. Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

Line Speed	Number of Defective Parts Found
20	22
20	21
30	20
30	17
40	15
40	16
50	14
50	11

What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? (a)There appears to be a positive relationship between line speed (feet per minute) and the number of defective parts.

(b)There appears to be a negative relationship between line speed (feet per minute) and the number of defective parts.

(c)There appears to be no noticeable relationship between line speed (feet per minute) and the number of defective parts.

Use the least squares method to develop the estimated regression equation.

=

Predict the number of defective parts found for a line speed of25feet per minute.

3.

xi	1	2	3	4	5
yi	3	8	5	11	12

The estimated regression equation for these data is =1.50+2.10x.

Compute SSE, SST, and SSR using equations SSE =(y_ii)², SST =(y_iy)², and SSR =(_iy)².

SSE=

SST=

SSR=

Compute the coefficient of determination r².

r²=

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

(a)The least squares line did not provide a good fit as a small proportion of the variability inyhas been explained by the least squares line.

(b)The least squares line did not provide a good fit as a large proportion of the variability inyhas been explained by the least squares line.

(c)The least squares line provided a good fit as a small proportion of the variability inyhas been explained by the least squares line.

(d)The least squares line provided a good fit as a large proportion of the variability inyhas been explained by the least squares line.

Compute the sample correlation coefficient. (Round your answer to three decimal places.)

4.

The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is

=21.655518+0.333445x, wherex= price ($)andy= overall score.

Brand	Price ($)	Score
A	180	76
B	150	73
C	95	61
D	70	58
E	70	38
F	35	24

Compute SST, SSR, and SSE. (Round your answers to three decimal places.)

SST=

SSR=

SSE=

Compute the coefficient of determination r². (Round your answer to three decimal places.)

r² =

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)

(a)The least squares line provided a good fit as a small proportion of the variability inyhas been explained by the least squares line.

(b)The least squares line provided a good fit as a large proportion of the variability inyhas been explained by the least squares line.

(c)The least squares line did not provide a good fit as a large proportion of the variability inyhas been explained by the least squares line.

(d)The least squares line did not provide a good fit as a small proportion of the variability inyhas been explained by the least squares line.

What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)