Question

1, An engineer wanted to determine how the weight of a car affects gas mileage. The accompanying data represent the weights of various domestic cars and their gas mileage in the city for a certain model year. Suppose that we add Car 12 to the original data. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Complete parts​(a) through​ (f) below.

Car	Weight (lbs)	Miles per Gallon
1	3765	19
2	3984	18
3	3590	21
4	3175	22
5	2580	27
6	3730	18
7	2605	26
8	3772	17
9	3310	20
10	2991	25
11	2752	26

(b) Compute the linear correlation coefficient with Car 12 included.

The linear correlation coefficient with Car 12 included is r =

​(Round to three decimal places as​ needed.)

(c) Compare the linear correlation coefficient of the part? (b) with the linear correlation coefficient for the original data. Why are the results here? reasonable?

i) The correlation coefficient changed significantly when Car 12 was added. This is reasonable since Car 12 does not follow the pattern of the original data.

ii) The correlation coefficients both indicate a strong negative correlation. This is reasonable since Car 12 does not follow the pattern of the original data.

iii) The correlation coefficients both indicate a strong negative correlation. This is reasonable since Car 12 roughly follows the pattern of the original data.

d) Now suppose that we add Car 13? (a hybrid? car) to the original data? (remove Car? 12). Car 13 weighs 2,890 pounds and gets 60 miles per gallon. Draw the scatter diagram with Car 13 included.

e) Compute the linear correlation coefficient with Car 13 included.

2, Researchers wondered whether the size of a​ person's brain was related to the​individual's mental capacity. They selected a sample of 5 females and 5 males and measured their MRI counts and IQ scores. The data is reported to the right. Complete parts ​(a) through ​(d) below.

Females_MRI	Females_IQ	Males_MRI	Males_IQ
951545	137	1001121	140
833868	132	1038438	139
856472	140	1079550	141
866662	130	924059	135
857782	133	949589	144

Critical Values for Correlation Coefficient

n
3	0.997
4	0.950
5	0.878
6	0.811
7	0.754
8	0.707
9	0.666
10	0.632
11	0.602
12	0.576
13	0.553
14	0.532
15	0.514
16	0.497
17	0.482
18	0.468
19	0.456
20	0.444
21	0.433
22	0.423
23	0.413
24	0.404
25	0.396
26	0.388
27	0.381
28	0.374
29	0.367
30	0.361

​(a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Choose the correct diagram below.

(b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly​ related? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

​(Round to three decimal places as​ needed.)

A.​Yes, MRI count and IQ are linearly related since the linear correlation coefficient is

B.​No, MRI count and IQ are not linearly related since the linear correlation coefficient is

​(c) Draw a scatter​ diagram, but use a different plotting symbol for each gender. Choose the correct diagram below.

​(d) Compute the linear correlation coefficient between MRI count and IQ for females. Compute the linear correlation coefficient between MRI count and IQ for males.

The linear correlation coefficient for females is

The linear correlation coefficient for males is

​(Round to three decimal places as​ needed.)

Answer 1

ANSWER:-

USING EXCEL

1)

A)

B)

The linear correlation coefficient with Car 12 included is r = -0.938

C)

The linear correlation coefficient with Car 12 excluded is r = -0.9604,so

The correlation coefficients both indicate a strong negative correlation. This is reasonable since Car 12 roughly follows the pattern of the original data.

D)

E)

Included car 18, Excel o/p is

So, the linear correlation coefficient with Car 13 included ,

r = -0.5070