Homework Answers
| Regression Statistics | ||||||
| Multiple R | 0.8622 | |||||
| R Square | 0.7435 | |||||
| Adjusted R Square | 0.7267 | |||||
| Standard Error | 4.2716 | |||||
| Observations | 50 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 3 | 2432.5128 | 810.8376 | 44.4385 | 0.0000 | |
| Residual | 46 | 839.3290 | 18.2463 | |||
| Total | 49 | 3271.8418 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 55.3878 | 2.4778 | 22.3536 | 0.0000 | 50.4002 | 60.3754 |
| Horsepower | -0.1437 | 0.0401 | -3.5853 | 0.0008 | -0.2244 | -0.0630 |
| Weight | -0.0046 | 0.0016 | -2.8401 | 0.0067 | -0.0079 | -0.0013 |
| Transmission | -3.6176 | 1.2838 | -2.8178 | 0.0071 | -6.2018 | -1.0334 |
(a)
The Significance F value of the F-test in ANOVA is 0.0000. This is less than the Type-I error 0.05. So, the null hypothesis that all the slope coefficients are equal to zero is rejected. So, the model, overall, is significant at a 5% level.
(b)
| Variable | P-value | Condition | Conclusion | Significant at 5%? |
| Horsepower | 0.0008 | < 0.05 | Null hypothesis that the slope is zero is rejected | Yes |
| Weight | 0.0067 | < 0.05 | Null hypothesis that the slope is zero is rejected | Yes |
| Transmission | 0.0071 | < 0.05 | Null hypothesis that the slope is zero is rejected | Yes |
7.
(a)
Coefficient of determination (R2) = 0.7435
(b)
SSR = 2432.5128
SST = 3271.8418
Coefficient of determination (R2) = 2432.5128 / 3271.8418 = 0.7435
(c)
Adjusted coefficient of determination (Adjusted R2) = 0.7267
(d)
In the case of multiple regression, using the R-squared value can lead to an erroneous conclusion. Even if one randomly ads a new independent variable that does not have any role in predicting the dependent variable, the R squared value will increase. Adding a number of independent variables will lead to move R squared value close to 1.0 even when the model itself will have no predicting value. So, to rectify this problem, the adjusted R squared value is referred to in the case of multiple-regression model. The adjustment is made by reducing the original R squared by reducing the degrees of freedom.
(e)
The percentage of variation of MPG that is fairly and truthfully explained by the model = 72.67%
(f)
Percentage unexplained = 100% - 72.67% = 27.33%
Add Answer to:
a.Overall, is this regression significant? Yes or no?
Explain, including the specific statistic or statistics that...
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...
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.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...
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,...
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...
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.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,”...
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...
1. For each of the following regression models, write down the X matrix and 3 vector....
1. For each of the following regression models, write down the X matrix and 3 vector. Assume in both cases that there are four observations (a) Y BoB1X1 + B2X1X2 (b) log Y Bo B1XiB2X2+ 2. For each of the following regression models, write down the X matrix and vector. Assume in both cases that there are five observations. (a) YB1XB2X2+BXE (b) VYBoB, X,a +2 log10 X2+E regression model never reduces R2, why 3. If adding predictor variables to a...
The systolic blood pressure of individuals is thought to be related to both age and weight....
The systolic blood pressure of individuals is thought to be related to both age and weight. For a random sample of 11 men, the following data were obtained Weight (pounds) Systolic Blood pressue Age (years) 149 132 52 173 143 59 184 153 67 194 162 73 211 154 64 196 16B 74 220 137 54 188 61 188 159 65 207 128 46 167 166 72 217 (a) Generate summary statistics, including the mean and standard deviation of each...
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...
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.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...
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,...
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...
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.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,”...
1. For each of the following regression models, write down the X matrix and 3 vector. Assume in both cases that there are four observations (a) Y BoB1X1 + B2X1X2 (b) log Y Bo B1XiB2X2+ 2. For each of the following regression models, write down the X matrix and vector. Assume in both cases that there are five observations. (a) YB1XB2X2+BXE (b) VYBoB, X,a +2 log10 X2+E regression model never reduces R2, why 3. If adding predictor variables to a...
The systolic blood pressure of individuals is thought to be related to both age and weight. For a random sample of 11 men, the following data were obtained Weight (pounds) Systolic Blood pressue Age (years) 149 132 52 173 143 59 184 153 67 194 162 73 211 154 64 196 16B 74 220 137 54 188 61 188 159 65 207 128 46 167 166 72 217 (a) Generate summary statistics, including the mean and standard deviation of each...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago