STATS HELP USING SPSS 3) (39pt) Consumer Research Inc. is an independent agency
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Question
STATS HELP USING SPSS
3) (39pt) Consumer Research Inc. is an independent agency that conducts research on consumer attitudes and behaviors for a variety of firms. In one study, a client asked for an investigation of consumer characteristics to explain the annual amount that credit card users charge on their accounts. Data collected on 50 credit card holders on explanatory variables income (in thousands of dollars), household size and dependent variable credit card amount expressed in dollars are portrayed on scatter plots below a. (2pt)Comment on the relationship of each explanatory variable to Credit card amount. MODEL 1-run a regression using income as the only explanatory variable a. (2pt)Comment on the goodness of fit of Model 1 - Model Summary Model 1 Std. Error Adjustedof the Model R R SquareR Square Estimate a. Predictors: (Constant), IncomeinThousandsExplanation / Answer
2. The scatterplot of income versus credit card amount shows a direction with points moving from lower left most corner to upper right most corner. Most of the points lie in and around the straight line (if drawn betwwen the points). The points lie close to each other, which indicates a moderate relationhsip between the variables. The scatterplot of household size shows overall positive linear association with moderate strength.
a. The coefficient of determination, R^2=39.8, which implies that around 39.8% variability in credit card amount is explained by the income.
b. The F(1,48)=31.751 and corresponding p value is 0.000. Per rejection rule based on p value, reject null hypothesis if p value is less than alpha=0.05. Here, p value is less than 0.05, therefore, reject H0 and conclude that income is an useful for predicting credit card amount.
c. Substitute the values of y-intercept (beta0), and slope (beta1) into the regression equation yhat=beta0+beta1x to obtain the least square regression equation.
Credit card amount=2204+40.480 Income
d. The y-intercept gives the value of the dependent variable for x=0. Thus, for no income, the credit card amount is $2204 (thousand). This is meaningless, therefore, interpreting intercept is not worthy in the context.
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