Tom's Used Mustangs: Regression Analysis
Regression Analysis (Tom’s Used Mustangs)
Irving Campus
GM 533: Applied Managerial Statistics
04/19/2012
Memo
To:
From:
Date: April 19st, 2012
Re: Statistic Analysis on price settings
Various hypothesis tests were compared as well as several multiple regressions in order to identify the factors that would manipulate the selling price of Ford Mustangs. The data being used contains observations on 35 used Mustangs and 10 different characteristics.
The test hypothesis that price is dependent on whether the car is convertible is superior to the other hypothesis tests conducted. The analysis performed showed that the test hypothesis with the smallest P-value was favorable, convertible cars had the smallest P-value.
The …show more content…
data that is used in this regression analysis to find the proper equation model for the relationship between price, age and mileage is from the Bryant/Smith Case 7 Tom’s Used Mustangs. As described in the case, the used car sales are determined largely by Tom’s gut feeling to determine his asking prices.
The most effective hypothesis test that exhibits a relationship with the mean price is if the car is convertible. The Regression Analysis is conducted to see if there is any relationship between the price and mileage, color, owner and age and GT. After running several models with different independent variables, it is concluded that there is a relationship between the price and mileage, price and age.
INTRODUCTION
The main objective of the report is to perform an analysis that will assist Tom in setting prices for used Mustangs in the near future. A statistic analysis was conducted to gain an enhanced understanding on the asking prices and the desired results will be achieved by hypothesis testing and multiple-regression analysis.
TESTING THE HYPOTHESIS
Hypothesis testing is appropriate to provide evidence in favor of some statement. The testing that will be performed will test whether there is a relationship or is not a relationship between mean price and convertible cars. Similar hypothesis testing will be carried out on the data set provide. The decision rule will be based on the P-value, which will determine how much uncertainty is casted on the null hypothesis by the sample data. Tom’s used Mustangs uses an alpha of 0.1 and this will be the benchmark for the P-value, any value less than 0.1 will lead to the rejection of the null hypothesis.
The first hypothesis test is with convertible cars, the table below displays the P-value of
the price against convertible cars.
P-value: Price vs Convertible Car | Predictor Coef SE Coef T P | Constant 7281.2 708.2 10.28 0.000 | CONVERT 3194 1325 2.41 0.022 |
Since the P-value is 0.022 and this value is smaller than 0.1, the null hypothesis will be rejected and this proves that there is sufficient evidence to claim that there is a relationship between the mean price and convertible cars, convertible cars do cause the price to change.
The second hypothesis test is with transmission type, the table below displays the P-value of price against transmission type.
. P-value: Price vs Color | Predictor Coef SE Coef T P | Constant 7098 1644 4.32 0.000 | COLOR 231.0 319.0 0.72 0.474 |
The P-value is 0.474 and this value is greater than 0.1, the null hypothesis cannot be rejected and this explains that there is insufficient evidence to claim that there is no relationship between price and color, the variation in color does not cause the price to change.
ANALYSIS AND METHODOLOGY Regression Analysis We conducted this to check whether the used Mustang’s prices depend on color, GT, owner, mileage or Age. We chose prices as the dependent variable and mileage and age as individual dependents. We ran several types of models, each with different variables. After running all models, we concluded that the best models were price vs. mileage and price vs. age. The reason behind choosing price vs. miles and price vs. age models is that their correlation coefficients R are 0.750 and 0.821 respectively, and the coefficients of determination for price vs. miles is R² = 0.562, and for price vs. age is R² = 0.674. The correlation coefficient R and coefficient of determination R² are far away from 1 in all other models.
Determination of R | .50 | Weak | .60 | Mildly Strong | .70 | Strong | .80 | Very strong | .90 | Extreme strong |
Regression Analysis: PRICE versus MILES
The regression equation is
PRICE = 12622 - 0.0917 MILES
Predictor Coef SE Coef T P
Constant 12621.7 804.7 15.68 0.000
MILES -0.09174 0.01410 -6.51 0.000
S = 2541.61 R-Sq = 56.2% R-Sq (adj) = 54.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 273526656 273526656 42.34 0.000
Residual Error 33 213172294 6459766
Total 34 486698950
Unusual Observations
Obs MILES PRICE Fit SE Fit Residual St Resid 22 89000 12000 4457 717 7543 3.09R
R denotes an observation with a large standardized residual.
The regression equation is: Y = 12622- 0.0917 xs, b0 = 12622 is the selling price of a used Mustang car. The slope is b1 = -0.0917, this is the amount of money that decreases the price of a used Mustang with an increase in its mileage. R2 =56.2, this means that about 56.2% of the variation in the price is explained by the variation in the mileage of the used Mustang. R = √ (0.562) = 0.750, this means there is a strong positive correlation between the price of a used Mustang and the mileage of the car. S = 2541.61 this is the standard error of the whole estimate. This tells us how the price values of a used Mustang vary from the predicted value of the used car being sold. The R-Sq (adj) = 0.549 this means that the 54.9 percent of used cars sold are “explained” by the mileage of the car.
The correlation coefficient R is greater than 0, this means that the correlation is positive.
P-value is 0.000; this means that there is extremely strong evidence of a relationship between the price of a used Mustang and the mileage of the car. We used the critical value F.05 based on 1 numerator and 33 denominator degrees of freedom. From the F table we find that at 95% critical value for Price vs. Miles = 4.139 while F = 42.34. Since the F (model) for Price vs. Miles = 42.34 which is greater than F.05 =4.139 we can reject the null hypothesis in favor of the alternative hypothesis at level of significance 0.05. The test tells us that if we reject the null hypothesis then we have evidence of a relationship between the prices vs. Miles of the used Mustangs. The Small P-value for the F test is evidence of a significant relationship between the …show more content…
variables.
Regression Analysis: PRICE versus AGE
The regression equation is
PRICE = 13727 - 1393 AGE
Predictor Coef SE Coef T P
Constant 13727.0 765.7 17.93 0.000
AGE -1393.2 168.7 -8.26 0.000
S = 2193.01 R-Sq = 67.4% R-Sq (adj) = 66.4%
Analysis of Variance
Source DF SS MS F P
Regression 1 327991650 327991650 68.20 0.000
Residual Error 33 158707299 4809312
Total 34 486698950
Unusual Observations
Obs AGE PRICE Fit SE Fit Residual St Resid 19 3.00 14500 9547 405 4953 2.30R
R denotes an observation with a large standardized residual.
The regression equation is Y = 13727 - 1393x, b0 = 13727, this is the price of a used Mustang. The slope b1 = -1393, this is the amount of money in dollars that the price decreases with an increase in the age of the car. R2 = 67.4, this means that about 67.4 % of the variation in price is explained by the variation in the age of the car. R = √ (0.674) = 0.821, this means there is a strong positive correlation between price and the age of a used Mustang car. The correlation is above 0 meaning that there is a positive correlation. S = 2193.01 this is the standard error of the whole estimate. This tells us how the price values of a used Mustang vary from the predicted value of the used car being sold. The R-Sq (adj) = 0.664 this means that the 66.4 percent of used cars sold are “explained” by the age of the car.
P-value is 0.000; this means that there is extremely strong evidence of a relationship between the price of a used Mustang and the age of the car being sold.
We used the critical value F.05 based on 1 numerator and 33 denominator degrees of freedom. From the F table we find that at 95% critical value for Price vs. Age = 4.139 while F = 68.20. Since the F (model) for Price vs. Age = 68.20 which is greater than F.05 =4.139 we can reject the null hypothesis in favor of the alternative hypothesis at level of significance 0.05.
ANALYSIS OF RESIDUALS
The following analysis of residuals was performed based on residual plots for prices against three predictors; miles, age and color. The residual plots tell us is that there isn't a violation of the regression assumptions, in the regression of demand on miles, age and color.
MULTICOLLINEARITY
Multicollinearity occurs if the independent variables in a regression situation if these independent variables are related to or dependent on each other. The data set would not be considered severe because none of the independent variables are at .9
Correlations: MILES, AGE, COLOR
MILES AGE
AGE 0.724
0.000
COLOR 0.032 -0.072
0.854 0.679
Cell Contents: Pearson correlation
P-Value
CONCLUSION
Tom’s used Mustangs will benefit the most by using the test hypothesis that provides the smallest P-value. The analysis conducted proves that the best test hypothesis compares the relationship between the mean price and convertible cars. The regression analysis is conducted to see if there is any relationship between the prices and mileage and age. After running several models with different independent variables, we concluded that there is a relationship between Prices vs. Mileage and Prices vs. Age.
Irving Campus
GM 533: Applied Managerial Statistics
04/19/2012
Memo
To:
From:
Date: April 19st, 2012
Re: Statistic Analysis on price settings
Various hypothesis tests were compared as well as several multiple regressions in order to identify the factors that would manipulate the selling price of Ford Mustangs. The data being used contains observations on 35 used Mustangs and 10 different characteristics.
The test hypothesis that price is dependent on whether the car is convertible is superior to the other hypothesis tests conducted. The analysis performed showed that the test hypothesis with the smallest P-value was favorable, convertible cars had the smallest P-value.
The …show more content…
data that is used in this regression analysis to find the proper equation model for the relationship between price, age and mileage is from the Bryant/Smith Case 7 Tom’s Used Mustangs. As described in the case, the used car sales are determined largely by Tom’s gut feeling to determine his asking prices.
The most effective hypothesis test that exhibits a relationship with the mean price is if the car is convertible. The Regression Analysis is conducted to see if there is any relationship between the price and mileage, color, owner and age and GT. After running several models with different independent variables, it is concluded that there is a relationship between the price and mileage, price and age.
INTRODUCTION
The main objective of the report is to perform an analysis that will assist Tom in setting prices for used Mustangs in the near future. A statistic analysis was conducted to gain an enhanced understanding on the asking prices and the desired results will be achieved by hypothesis testing and multiple-regression analysis.
TESTING THE HYPOTHESIS
Hypothesis testing is appropriate to provide evidence in favor of some statement. The testing that will be performed will test whether there is a relationship or is not a relationship between mean price and convertible cars. Similar hypothesis testing will be carried out on the data set provide. The decision rule will be based on the P-value, which will determine how much uncertainty is casted on the null hypothesis by the sample data. Tom’s used Mustangs uses an alpha of 0.1 and this will be the benchmark for the P-value, any value less than 0.1 will lead to the rejection of the null hypothesis.
The first hypothesis test is with convertible cars, the table below displays the P-value of
the price against convertible cars.
P-value: Price vs Convertible Car | Predictor Coef SE Coef T P | Constant 7281.2 708.2 10.28 0.000 | CONVERT 3194 1325 2.41 0.022 |
Since the P-value is 0.022 and this value is smaller than 0.1, the null hypothesis will be rejected and this proves that there is sufficient evidence to claim that there is a relationship between the mean price and convertible cars, convertible cars do cause the price to change.
The second hypothesis test is with transmission type, the table below displays the P-value of price against transmission type.
. P-value: Price vs Color | Predictor Coef SE Coef T P | Constant 7098 1644 4.32 0.000 | COLOR 231.0 319.0 0.72 0.474 |
The P-value is 0.474 and this value is greater than 0.1, the null hypothesis cannot be rejected and this explains that there is insufficient evidence to claim that there is no relationship between price and color, the variation in color does not cause the price to change.
ANALYSIS AND METHODOLOGY Regression Analysis We conducted this to check whether the used Mustang’s prices depend on color, GT, owner, mileage or Age. We chose prices as the dependent variable and mileage and age as individual dependents. We ran several types of models, each with different variables. After running all models, we concluded that the best models were price vs. mileage and price vs. age. The reason behind choosing price vs. miles and price vs. age models is that their correlation coefficients R are 0.750 and 0.821 respectively, and the coefficients of determination for price vs. miles is R² = 0.562, and for price vs. age is R² = 0.674. The correlation coefficient R and coefficient of determination R² are far away from 1 in all other models.
Determination of R | .50 | Weak | .60 | Mildly Strong | .70 | Strong | .80 | Very strong | .90 | Extreme strong |
Regression Analysis: PRICE versus MILES
The regression equation is
PRICE = 12622 - 0.0917 MILES
Predictor Coef SE Coef T P
Constant 12621.7 804.7 15.68 0.000
MILES -0.09174 0.01410 -6.51 0.000
S = 2541.61 R-Sq = 56.2% R-Sq (adj) = 54.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 273526656 273526656 42.34 0.000
Residual Error 33 213172294 6459766
Total 34 486698950
Unusual Observations
Obs MILES PRICE Fit SE Fit Residual St Resid 22 89000 12000 4457 717 7543 3.09R
R denotes an observation with a large standardized residual.
The regression equation is: Y = 12622- 0.0917 xs, b0 = 12622 is the selling price of a used Mustang car. The slope is b1 = -0.0917, this is the amount of money that decreases the price of a used Mustang with an increase in its mileage. R2 =56.2, this means that about 56.2% of the variation in the price is explained by the variation in the mileage of the used Mustang. R = √ (0.562) = 0.750, this means there is a strong positive correlation between the price of a used Mustang and the mileage of the car. S = 2541.61 this is the standard error of the whole estimate. This tells us how the price values of a used Mustang vary from the predicted value of the used car being sold. The R-Sq (adj) = 0.549 this means that the 54.9 percent of used cars sold are “explained” by the mileage of the car.
The correlation coefficient R is greater than 0, this means that the correlation is positive.
P-value is 0.000; this means that there is extremely strong evidence of a relationship between the price of a used Mustang and the mileage of the car. We used the critical value F.05 based on 1 numerator and 33 denominator degrees of freedom. From the F table we find that at 95% critical value for Price vs. Miles = 4.139 while F = 42.34. Since the F (model) for Price vs. Miles = 42.34 which is greater than F.05 =4.139 we can reject the null hypothesis in favor of the alternative hypothesis at level of significance 0.05. The test tells us that if we reject the null hypothesis then we have evidence of a relationship between the prices vs. Miles of the used Mustangs. The Small P-value for the F test is evidence of a significant relationship between the …show more content…
variables.
Regression Analysis: PRICE versus AGE
The regression equation is
PRICE = 13727 - 1393 AGE
Predictor Coef SE Coef T P
Constant 13727.0 765.7 17.93 0.000
AGE -1393.2 168.7 -8.26 0.000
S = 2193.01 R-Sq = 67.4% R-Sq (adj) = 66.4%
Analysis of Variance
Source DF SS MS F P
Regression 1 327991650 327991650 68.20 0.000
Residual Error 33 158707299 4809312
Total 34 486698950
Unusual Observations
Obs AGE PRICE Fit SE Fit Residual St Resid 19 3.00 14500 9547 405 4953 2.30R
R denotes an observation with a large standardized residual.
The regression equation is Y = 13727 - 1393x, b0 = 13727, this is the price of a used Mustang. The slope b1 = -1393, this is the amount of money in dollars that the price decreases with an increase in the age of the car. R2 = 67.4, this means that about 67.4 % of the variation in price is explained by the variation in the age of the car. R = √ (0.674) = 0.821, this means there is a strong positive correlation between price and the age of a used Mustang car. The correlation is above 0 meaning that there is a positive correlation. S = 2193.01 this is the standard error of the whole estimate. This tells us how the price values of a used Mustang vary from the predicted value of the used car being sold. The R-Sq (adj) = 0.664 this means that the 66.4 percent of used cars sold are “explained” by the age of the car.
P-value is 0.000; this means that there is extremely strong evidence of a relationship between the price of a used Mustang and the age of the car being sold.
We used the critical value F.05 based on 1 numerator and 33 denominator degrees of freedom. From the F table we find that at 95% critical value for Price vs. Age = 4.139 while F = 68.20. Since the F (model) for Price vs. Age = 68.20 which is greater than F.05 =4.139 we can reject the null hypothesis in favor of the alternative hypothesis at level of significance 0.05.
ANALYSIS OF RESIDUALS
The following analysis of residuals was performed based on residual plots for prices against three predictors; miles, age and color. The residual plots tell us is that there isn't a violation of the regression assumptions, in the regression of demand on miles, age and color.
MULTICOLLINEARITY
Multicollinearity occurs if the independent variables in a regression situation if these independent variables are related to or dependent on each other. The data set would not be considered severe because none of the independent variables are at .9
Correlations: MILES, AGE, COLOR
MILES AGE
AGE 0.724
0.000
COLOR 0.032 -0.072
0.854 0.679
Cell Contents: Pearson correlation
P-Value
CONCLUSION
Tom’s used Mustangs will benefit the most by using the test hypothesis that provides the smallest P-value. The analysis conducted proves that the best test hypothesis compares the relationship between the mean price and convertible cars. The regression analysis is conducted to see if there is any relationship between the prices and mileage and age. After running several models with different independent variables, we concluded that there is a relationship between Prices vs. Mileage and Prices vs. Age.