GM 533: Applied Managerial Statistics
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 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
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...