p. 186: 35, 36 p. 216: 36abcd, 57*, 58 (*also create a scatter diagram and find r to analyze the data) p. 278: 12abce

Transcription

1 STAT E-50 - Introduction to Statistics SPSS4 Solutions p. 186: 35, 36 p. 216: 36abcd, 57*, 58 (*also create a scatter diagram and find r to analyze the data) p. 278: 12abce p. 186: 35 a) b) The relationship is linear, negative, and strong, and there don't seem to be any outliers. c) r = Correlations Highway Gas Horsepower Mileage (mpg) Horsepower Pearson Correlation ** Sig. (2-tailed).000 N Highway Gas Mileage (mpg) Pearson Correlation ** 1 Sig. (2-tailed).000 N **. Correlation is significant at the 0.01 level (2-tailed). d) Cars with higher horsepower tend have lower fuel economy (i.e. fewer mpg).

2 p. 186: 36 a) b) r =.934 Correlations Marijuana (%) Other Drugs (%) Marijuana (%) Pearson Correlation ** Sig. (2-tailed).000 N Other Drugs (%) Pearson Correlation.934 ** 1 Sig. (2-tailed).000 N **. Correlation is significant at the 0.01 level (2-tailed). c) The relationship is linear, positive, and very strong d) No - there is an association between the percent of teens who have used marijuana and the percent of teen who have used other drugs, but correlation doesn t imply a causal relationship. Page 2

3 p. 216: 36 a) A regression model is appropriate: both of the variables are quantitative, and the scatterplot shows a fairly constant linear relationship with no outliers. b) The equation of the regression line is Mortgages = Interest Rate Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) Interest.Rate a. Dependent Variable: Mortgages (in millions dollars) c) The predicted mortgage amount for an interest rate of 20% is $65.39 million d) This is not an appropriate prediction because the value of 20% is well outside of the range of the given data. Page 3

4 p. 216: 57 a) %Body Fat =.250 Weight Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) Weight a. Dependent Variable: %Body Fat b) A linear model appears to be appropriate. The scatterplot shows a fairly strong positive linear relationship between the variables. c) The slope of the regression line is.250. This tells us that the body fat will increase by about.25% for every additional pound of weight. Page 4

5 d) The model may not be likely to make reliable estimates. Since R 2 =.485, only 48.5% of the variability in % body fat can be accounted for by the model. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), Weight e) The residual for a person who weighs 190 and has 21% body fat is.86% Additional questions: The Model Summary shows that r =.697; the scatter diagram is shown in part b. Page 5

6 p. 216: 58 The scatterplot with Waist as the predictor variable shows a strong positive linear relationship. The linear model for this relationship is %Body Fat = 2.22 Waist For each additional inch in waist size, the model predicts an increase of 2.22% body fat. The value of R 2 for this model is.787 indicating that 78.7% of the variability in % body fat can be accounted for by the model. This is higher than the value when Weight is the predictor (R 2 =.485), indicating that this model is a more powerful predictor than the model based on weight. Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) Waist a. Dependent Variable: %Body Fat Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate a a. Predictors: (Constant), Waist b. Dependent Variable: %Body Fat Page 6

7 p. 278: 12 a) The correlation between the Friday scores and the Monday scores is r =.473 Correlations Fri Mon Fri Pearson Correlation * Sig. (2-tailed).017 N Mon Pearson Correlation.473 * 1 Sig. (2-tailed).017 N *. Correlation is significant at the 0.05 level (2-tailed). b) The scatter diagram shows a weak positive linear association between the Friday score and the Monday score. Generally, students who scored high on Friday also tended to score high on Monday. c) A student with a positive residual scored higher on Monday's test than the model predicted. Page 7

8 e) The regression equation is Monday = Friday Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) Fri a. Dependent Variable: Mon f) According to the model a student who scored 40 on Friday is expected to have a Monday score of about 36. Page 8