Use excels data analysis tool to preform a regression on the following set on numbers. Post...
Use excels data analysis tool to preform a regression on the following set on numbers. Post your results. Then answer the following questions.
A consumer Organization want to develop a regression model to predict gasoline mileage (as measured by miles per gallon) based on horsepower of the car's engine and the weight of the car, in pounds. A sample of 50 percent recent car models was selected, with the results recorded.
1. State the multiple regression equation.
2. Interpret the meaning of the slopes, b and b2 in this problem.
3. Explain why the regression coefficient b0, has no practical meaning in the context of this problem
4. Predict the mean miles per gallon for cars that have 60 horsepower and weigh 2000 pounds.
| MPG | Horsepower | Weight |
| 43.1 | 48 | 1985 |
| 19.9 | 110 | 3365 |
| 19.2 | 105 | 3535 |
| 17.7 | 165 | 3445 |
| 18.1 | 139 | 3205 |
| 20.3 | 103 | 2830 |
| 21.5 | 115 | 3245 |
| 16.9 | 155 | 4360 |
| 15.5 | 142 | 4054 |
| 18.5 | 150 | 3940 |
| 27.2 | 71 | 3190 |
| 41.5 | 76 | 2144 |
| 46.6 | 65 | 2110 |
| 23.7 | 100 | 2420 |
| 27.2 | 84 | 2490 |
| 39.1 | 58 | 1755 |
| 28.0 | 88 | 2605 |
| 24.0 | 92 | 2865 |
| 20.2 | 139 | 3570 |
| 20.5 | 95 | 3155 |
| 28.0 | 90 | 2678 |
| 34.7 | 63 | 2215 |
| 36.1 | 66 | 1800 |
| 35.7 | 80 | 1915 |
| 20.2 | 85 | 2965 |
| 23.9 | 90 | 3420 |
| 29.9 | 65 | 2380 |
| 30.4 | 67 | 3250 |
| 36.0 | 74 | 1980 |
| 22.6 | 110 | 2800 |
| 36.4 | 67 | 2950 |
| 27.5 | 95 | 2560 |
| 33.7 | 75 | 2210 |
| 44.6 | 67 | 1850 |
| 32.9 | 100 | 2615 |
| 38.0 | 67 | 1965 |
| 24.2 | 120 | 2930 |
| 38.1 | 60 | 1968 |
| 39.4 | 70 | 2070 |
| 25.4 | 116 | 2900 |
| 31.3 | 75 | 2542 |
| 34.1 | 68 | 1985 |
| 34.0 | 88 | 2395 |
| 31.0 | 82 | 2720 |
| 27.4 | 80 | 2670 |
| 22.3 | 88 | 2890 |
| 28.0 | 79 | 2625 |
| 17.6 | 85 | 3465 |
| 34.4 | 65 | 3465 |
| 20.6 | 105 | 3380 |
Homework Answers
Add Answer to:
Use excels
data analysis tool to preform a regression on the following set on
numbers. Post...
An analyst at a consumer organization must develop a regression model to predict fuel economy (also...
An
analyst at a consumer organization must develop a regression model
to predict fuel economy (also referred to as gasoline mileage) of
automobiles measured in miles per gallon (mpg) based on the
horsepower of its engine, the weight of the car (in pounds) and the
type of transmission (manual or automatic). The data for 50
randomly selected automobiles is presented in the table below. Fit
a multiple regression model for gasoline mileage as it depends on
engine horsepower, vehicle weight,...
Perform simple linear regression model for gasoline mileage as it depends on horsepower alone. Present a...
Perform simple linear regression model for gasoline mileage as
it depends on horsepower alone. Present a copy of this regression
output report.
a.State (here) this simple linear regression equation.
b.Overall, is this regression significant? Choose yes or no
and explain the reason for your choice.
c.Comment on the significance of the variable
coefficient.
d.How much of the variation in mpg is fairly represented by
this model?
MPG 43.1 19.9 19.2 Horsepower 48 110 105 165 139 103 115 155 142...
a.Present (here) the plot of the residuals of this simple linear regression model against its fitted...
a.Present (here) the plot of the residuals of this simple
linear regression model against its fitted values.
b. Describe (here) the appearance of this residual
plot.
c.State (here) the RMSE of this regression.
MPG 43.1 19.9 19.2 Horsepower 48 110 105 165 139 103 115 155 142 150 71 76 65 100 84 58 88 92 139 110 90 17.7 18.1 20.3 21.5 16.9 ISS 185 27.2 41.5 46.6 23.7 27.2 39.1 28.0 24.0 20.2 20.5 28.0 34.7 36.1 35.7...
Perform another multiple regression model for gasoline mileage as it depends on the set of independent...
Perform another multiple regression model for gasoline mileage
as it depends on the set of independent variables retained from
part 12.e (use the same definitions of the variables as you used in
part 1).
• Present a copy of this regression output report.
a.State (here) this multiple regression equation.
b.Overall, is this regression significant?
c.Comment on the significance of each individual variable
coefficient.
d.How much of the variation in mpg is fairly represented by
this model?
a.Present the plot of...
a.Predict the gasoline mileage for a vehicle that has a 105 horsepower engine, weighs 3380 pounds,...
a.Predict the gasoline mileage for a vehicle that has a 105
horsepower engine, weighs 3380 pounds, and has a manual
transmission.
b.What is the residual in gasoline mileage between the mpg
calculated in part 9.a and the actual gasoline mileage for this
vehicle as listed in the data table?
c.State two reasons why the result calculated in part 9.a is
different from the actual gasoline mileage for this vehicle as
listed in the data table.
Transmission manual MPG 43.1 19.9...
a.Overall, is this regression significant? Yes or no? Explain, including the specific statistic or statistics that...
a.Overall, is this regression significant? Yes or no?
Explain, including the specific statistic or statistics that were
used and how they were used.
b.Is each individual variable coefficient significant? Yes
or no for each variable. Explain for each variable, including the
specific statistic or statistics that were used and how they were
used.
7.a.State (here) the value of the coefficient of
determination for this model.
b.Show (here) that this coefficient is numerically equal to
SSR/SST.
c.State (here) the value of...
a.State (here) in words the specific meaning of the numerical value of the regression coefficient on...
a.State
(here)
in words
the specific
meaning of
the numerical
value of the regression
coefficient on engine
horsepower in terms of
what it measuresfor this
problem.
Does this
coefficient make sense, according to what you would expect for
it?
b.State
(here)
in words
the specific
meaning of
the numerical
value of the regression
coefficient on
weight in terms of
what it measures for this
problem.
(In other
words, what does this number measure and how much?)
• Does this
coefficient...
a.Calculate and present the variance inflation factor, VIF, for each predictor variable. b.Based on VIF, which,...
a.Calculate and present the variance inflation factor, VIF,
for each predictor variable.
b.Based on VIF, which, if any, of any of the independent
variables are related to each other such an extent that you suspect
that they are not truly independent of each other. Why?
c.Based on VIF, is multicollinearity a problem? Briefly
explain why?
d.If your answer to part 12.c is “yes,” do you recommend
deleting any of the predictor variables?
e.If your answer to part 12.d is “yes,”...
9. a. Predict the gasoline mileage for a vehicle that has a 105 horsepower engine, weighs...
9. a. Predict the gasoline mileage for a vehicle that has a 105
horsepower engine, weighs 3380 pounds, and has a manual
transmission.
Manual: MPG (Y) = 51.77 - 0.1437 Horsepower (X1) - 0.00460
Weight (X2)
= 51.77-0.1437(105)-0.00460(3380) = 21.133
b. What is the residual in gasoline mileage between the mpg
calculated in part 9.a and the actual gasoline mileage for this
vehicle as listed in the data table?
c. State two reasons why the result calculated in part 9.a...
2. Using the data set of the Health Exam Results, conduct the following analysis between the variables of weight (WT) and Body Mass Index (BMI). Number the data set from 1 to 40, and select the...
2. Using the data set of the Health Exam Results, conduct the following analysis between the variables of weight (WT) and Body Mass Index (BMI). Number the data set from 1 to 40, and select the following individuals: . Set 1 (Malo): 1, 5, 10, 13, 15, 18, 19, 24, 29, 31, 32, 33 .Set 2 (Fomalo): 4, 9, 15, 16, 17, 22, 23, 29, 33, 37, 38, 40 Draw a scatter diagram of the sample of 12 data set...
An
analyst at a consumer organization must develop a regression model
to predict fuel economy (also referred to as gasoline mileage) of
automobiles measured in miles per gallon (mpg) based on the
horsepower of its engine, the weight of the car (in pounds) and the
type of transmission (manual or automatic). The data for 50
randomly selected automobiles is presented in the table below. Fit
a multiple regression model for gasoline mileage as it depends on
engine horsepower, vehicle weight,...
Perform simple linear regression model for gasoline mileage as
it depends on horsepower alone. Present a copy of this regression
output report.
a.State (here) this simple linear regression equation.
b.Overall, is this regression significant? Choose yes or no
and explain the reason for your choice.
c.Comment on the significance of the variable
coefficient.
d.How much of the variation in mpg is fairly represented by
this model?
MPG 43.1 19.9 19.2 Horsepower 48 110 105 165 139 103 115 155 142...
a.Present (here) the plot of the residuals of this simple
linear regression model against its fitted values.
b. Describe (here) the appearance of this residual
plot.
c.State (here) the RMSE of this regression.
MPG 43.1 19.9 19.2 Horsepower 48 110 105 165 139 103 115 155 142 150 71 76 65 100 84 58 88 92 139 110 90 17.7 18.1 20.3 21.5 16.9 ISS 185 27.2 41.5 46.6 23.7 27.2 39.1 28.0 24.0 20.2 20.5 28.0 34.7 36.1 35.7...
Perform another multiple regression model for gasoline mileage
as it depends on the set of independent variables retained from
part 12.e (use the same definitions of the variables as you used in
part 1).
• Present a copy of this regression output report.
a.State (here) this multiple regression equation.
b.Overall, is this regression significant?
c.Comment on the significance of each individual variable
coefficient.
d.How much of the variation in mpg is fairly represented by
this model?
a.Present the plot of...
a.Predict the gasoline mileage for a vehicle that has a 105
horsepower engine, weighs 3380 pounds, and has a manual
transmission.
b.What is the residual in gasoline mileage between the mpg
calculated in part 9.a and the actual gasoline mileage for this
vehicle as listed in the data table?
c.State two reasons why the result calculated in part 9.a is
different from the actual gasoline mileage for this vehicle as
listed in the data table.
Transmission manual MPG 43.1 19.9...
a.Overall, is this regression significant? Yes or no?
Explain, including the specific statistic or statistics that were
used and how they were used.
b.Is each individual variable coefficient significant? Yes
or no for each variable. Explain for each variable, including the
specific statistic or statistics that were used and how they were
used.
7.a.State (here) the value of the coefficient of
determination for this model.
b.Show (here) that this coefficient is numerically equal to
SSR/SST.
c.State (here) the value of...
a.State
(here)
in words
the specific
meaning of
the numerical
value of the regression
coefficient on engine
horsepower in terms of
what it measuresfor this
problem.
Does this
coefficient make sense, according to what you would expect for
it?
b.State
(here)
in words
the specific
meaning of
the numerical
value of the regression
coefficient on
weight in terms of
what it measures for this
problem.
(In other
words, what does this number measure and how much?)
• Does this
coefficient...
a.Calculate and present the variance inflation factor, VIF,
for each predictor variable.
b.Based on VIF, which, if any, of any of the independent
variables are related to each other such an extent that you suspect
that they are not truly independent of each other. Why?
c.Based on VIF, is multicollinearity a problem? Briefly
explain why?
d.If your answer to part 12.c is “yes,” do you recommend
deleting any of the predictor variables?
e.If your answer to part 12.d is “yes,”...
9. a. Predict the gasoline mileage for a vehicle that has a 105
horsepower engine, weighs 3380 pounds, and has a manual
transmission.
Manual: MPG (Y) = 51.77 - 0.1437 Horsepower (X1) - 0.00460
Weight (X2)
= 51.77-0.1437(105)-0.00460(3380) = 21.133
b. What is the residual in gasoline mileage between the mpg
calculated in part 9.a and the actual gasoline mileage for this
vehicle as listed in the data table?
c. State two reasons why the result calculated in part 9.a...
2. Using the data set of the Health Exam Results, conduct the following analysis between the variables of weight (WT) and Body Mass Index (BMI). Number the data set from 1 to 40, and select the following individuals: . Set 1 (Malo): 1, 5, 10, 13, 15, 18, 19, 24, 29, 31, 32, 33 .Set 2 (Fomalo): 4, 9, 15, 16, 17, 22, 23, 29, 33, 37, 38, 40 Draw a scatter diagram of the sample of 12 data set...
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