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
Acceleration MPG 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 47
Chevrolet Malibu Hybrid 8 41
Hyundai Sonata Hybrid SE 8.2 39
Ford Fusion SE Hybrid 8.3 39
Toyota Camry LE(4-cyl.) 8 32
Nissan Altima 2.5 SV 7.6 31
Honda Accord EX(1.5T) 7.7 31
Chevrolet Malibu LT(1.5T) 8.4 29
Kia Optima EX(4-cyl.) 8 28
Hyundai Sonata SEL(4-cyl.) 8.3 28
Volkswagen Passat SE(4-cyl.) 8.6 28
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 Momheight Dadheight Outlier? Prediction Error
66 66 71
64 62 68
64 65 70 Five Number Summary for Height
69 66 76 Minimum:
66 63 70 1st quartile:
63 61 68 Median:
68 64 69 3rd quartile:
65 62 66 Maximum:
64 70 73
65 70 75 Outlier Parameters
66 63 70 IQR:
68 68 69 Lower Limit
66 60 77 Upper Limit
60 61 65 # of outliers
60 59 62
60 62 63
64 60 72
70 62 74
64 61 70
63 61 70
61 60 67
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
67.5 69 69
62 60 60
64 63 74
63 62 68
64 62 69
63 58 74
62.5 65 71.5
65 64 72
66.5 63 74
69.5 66 72
63.5 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
65.5 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
64.5 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 57 65
64 62 63
66 66 73
65 64 67
67 65 70
64.5 66 70
70 65 77
63 56 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
59.5 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
60.5 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
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
Triceps Thigh Midarm Bodyfat z-score outlier?
19.5 43.1 29.1 11.9
24.7 49.8 28.2 22.8
30.7 51.9 37 18.7
29.8 54.3 31.1 20.1 Outlier Parameters Calculate for Bodyfat Column
19.1 42.2 30.9 12.9 IQR: mean:
25.6 53.9 23.7 21.7 Lower Limit median:
31.4 58.5 27.6 27.1 Upper Limit mode:
27.9 52.1 30.6 25.4 # of outliers standard deviation:
22.1 49.9 23.2 21.3 # of outliers
25.5 53.5 24.8 19.3
31.1 56.6 30 25.4
30.4 56.7 28.3 27.2
18.7 46.5 23 11.7
19.7 44.2 28.6 17.8
14.6 42.7 21.3 12.8
29.5 54.4 30.1 23.9
27.7 55.3 25.7 22.6
30.2 58.6 24.6 25.4
22.7 48.2 27.1 14.8
25.2 51 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:
