math

Please complete the following activities contained within the Excel sheet. 

Linear Regression Task

Instructions for Excel Practical: First attempt the linear regression task. Please use the data that is on the following slide, titled “Assignment Data” to complete the first part of the assignment. Then follow up with the next two tabs to perform a multiple regression using Excel. The first multiple regression example is already completed for you in the Lecture.
Part 1: Complete the following Task

Create a scatterplot of the data on the next tab. Be sure to label the axes and include a regression line. Be sure to include the equation and r-squared value and place it on the top right of the graph.
Part 2: Interpret your results: please type in your answers to the following questions. Be sure to fully elaborate on them and try to include at least 2-3 sentences to explain each part.
A. What kind of correlation (positive, negative, or no correlation) exists between the

MPG

of a car and its acceleration time? Is it a strong correlation?

B. What are the degrees of freedom of the data set? Using the critical values table in the Lecture, is the R-squared Statistic significant enough for us to make any statistical inferences? If not, how large should the sample be to substantiate the results of this study?

C. Should we interpret the y-intercept in this case? Why or why not?

D. Using your equation, predict the MPG of a car that accelerates in 7.5 seconds.

E. In a few sentences, summarize the findings of this study? What effect does MPG consumption have on the acceleration time of a vehicle?

Linear Regression Data

MPG

47

8

39

8

31

8

8.3 28

28

Acceleration	Data retrieved from: https://www.consumerreports.org/fuel-economy-efficiency/vehicle-fuel-economy-vs-performance/
Honda Accord Hybrid EX	7.4		47
Toyota Camry Hybrid LE	7.			8
Chevrolet Malibu Hybrid	41
Hyundai Sonata Hybrid SE	8.2		39
Ford Fusion SE Hybrid		8.3
Toyota Camry LE (4-cyl.)	32
Nissan Altima 2.5 SV	7.6		31
Honda Accord EX (1.5T)	7.7
Chevrolet Malibu LT (1.5T)	8.4	29
Kia Optima EX (4-cyl.)			28
Hyundai Sonata SEL (4-cyl.)
Volkswagen Passat SE (4-cyl.)	8.6

https://www.consumerreports.org/cars/honda/accord

https://www.consumerreports.org/cars/kia/optima

https://www.consumerreports.org/cars/hyundai/sonata

https://www.consumerreports.org/cars/volkswagen/passat

https://www.consumerreports.org/cars/toyota/camry

https://www.consumerreports.org/cars/chevrolet/malibu

https://www.consumerreports.org/cars/hyundai/sonata

https://www.consumerreports.org/cars/ford/fusion

https://www.consumerreports.org/cars/toyota/camry

https://www.consumerreports.org/cars/nissan/altima

https://www.consumerreports.org/cars/honda/accord
https://www.consumerreports.org/cars/chevrolet/malibu

Mult Regression_

Height

Height

66

64

66

66

70

63

68

68 64 69

65 62 66

64 70

65 70

66 63 70

68 68 69

66

60 61 65

60

62

60 62 63
64 60

70 62

64 61 70
63 61 70
61 60

69 65 68
63 64 65
66 66 66
65 64 70

64 62 68

66 64 73
65 61 67
63 60 67
63 64 74
65 62 75
66 64 70
67 64 70

69 69

62 60 60
64 63 74
63 62 68
64 62 69
63

74

65

65 64 72

63 74

66 72

60 67

69 64 74
67 63 72
67 66 70
67 69 66
67 65 68
67 63 71
63 60 69
63 61 67
60 60 66
63 68 75

62 71

66 63 72
68 67 70
65 62 67
65 63.5 69
66 67 70
62 63 69
66 65 68
67 64 71

63 61 70

66 60 69
67 62 71
61 63 69
62 60 68
63.5 62 63
61 62 65
64 61 63
61 65 69
61 64 68
63 61 72
62 62 72
64 64 74

64 62 68

65 66 73
64 61 67
59 60 64
65 67 68
63 65 68

62 66.5

64 63 71
70 62 76
60 61 65
69 68 73
62 63 68
65 69 72
64 62 66
64 64 70
66 61 70

63 62 68

67 68 69
60 60 68
68 67 72
67 70 76
66 60 71
67 68 72

65 64 70

61 64 64
64 63 72
68 64 71

64 63 71

65.5 62 70

67 66 70

67 69 74
62.5 65.5 68
62 61 65
62

65

64 62 63
66 66 73
65 64 67
67 65 70
64.5 66 70
70 65 77
63

62

65 64 71
60 64 69
69 64 75
64 63 67
62 62 66
63 62 65
64 69 70
62 62 68
72 65 72

63 60 69
67 69 66

68 64 67
72 70 76

59 65

65 70 70
68 60 70
61 59 67
66 64 69
62.5 67 71.5
65 62 70
65 63 70
63 61 65
70 68 71
64 64 67
63 65 66
68 69 72
63.5 64 69
67.5 70 72
66 65 71

66 63 72

61 61 65
63 65 72

61 60 67

61 60 62
66 65 70
63 61 63
66 62 67
66 62 68
68 63 69

62 62 68
66 67 70

63 62 69
66 62 72
66 65 69
69 66 70
68 65 73
64 65 74
69 67 74

65 63 70

67 64 69
66 67 67
63 62 70
61 66 66
67 64 72

67 63 71

63.5 65 71
60 64 66

67 65 68

61 59 70
63 65 64
62 64 66
67 66 71
60 62 65
64.5 65.5 66

62 67

69.5 63 74
66 64 74

65 62 67

63 60 72
68 66 74
68 62 71
65 63 71

63 65 68

62 60 67
63 66 68
71 69 72
63 63 68
63 63 66

62 64 66
63 61 67
65 67 68

65 64 73
64 58 72
68 68 72
64 63 68
61 62 67
62 60 66
66 62 71
68 66 72
65 64 68
69 65 75

65 69 72

64 68 72

64 64 70
67 62 71

68 65 67
73 68 76

Momheight	Dadheight	Outlier?	Prediction	Error
																																																							66																				71
																																																													64																																																							62																																																		68
																																																									65																																									70	Five Number Summary for Height
																																			69					76	Minimum:
																																																										63	1st quartile:
																													61	Median:
3rd quartile:
Maximum:
							73
				75		Outlier Parameters
	IQR:
	Lower Limit
																													60		77		Upper Limit
		# of outliers
				59
																										72
												74
																																																		67
	67.5
	58
		62.5		71.5
	66.5
	69.5
				63.5
			65.5
		64.5
57
56
59.5
60.5

Attribution: n=214 female students at University of California at Davis

Please perform the multiple regression for each of these tabs and do not delete them. Please include the output of your regressions to this assignment.

Mult Regression_

Bodyfat

Bodyfat

.7

.9

Outlier Parameters

IQR:

.7

Lower Limit

Upper Limit

# of outliers

# of outliers

31.1

30 25.4

18.7

23

21.3

25.4

27.1

51

Triceps	Thigh	Midarm	z-score	outlier?
19.5	43.1	29.1	11.9
24.7	49.8	28.2	22.8
	30		51	37		18.7
29.8	54.3		31.1	20.1	Calculate for Bodyfat Column
19.1	42.2	30.9	12.9	mean:
25.6	53.9		23	21.7	median:
31.4	58.5	27.6		27.1	mode:
27.9	52.1	30.6			25.4	standard deviation:
22.1	49.9	23.2		21.3
25.5	53.5	24.8	19.3
56.6
30.4	56.7	28.3	27.2
46.5	11.7
19.7	44.2	28.6	17.8
14.6	42.7	12.8
29.5	54.4	30.1	23.9
27.7	55.3	25.7	22.6
30.2	58.6	24.6
22.7	48.2	14.8
25.2	27.5	21.1

Attribution: Data source: Applied Regression Models, (4th edition), Kutner, Neter, and Nachtsheim

Run a multiple regression that predicts bodyfat based on midarm, thigh, and triceps measurements.
Write your equation here:
Using the model, provided, find the predicted body fat of someone who has a triceps measurement of 21.4, thigh of 45.6, and midarm measurement of 27.6. Show your work below: