Correlations. Regression. Page 1. Correlations SQUAREFO BEDROOMS BATHS ASKINGPR

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4 Correlations SQUAREFO BEDROOMS BATHS ASKINGPR Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Correlations **. Correlation is significant at the 0.0 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed). SQUAREFO BEDROOMS BATHS ASKINGPR.79**.73**.749** **.759**.738** **.759**.669* **.738**.669* Regression Variables Entered/Removed b Variables Entered BATHS, SQUAREF O, BEDROOM S a Variables Removed a. All requested variables entered. b. Dependent Variable: ASKINGPR. Enter Method Summary b R R Square Adjusted R Square Std. Error of the Estimate.790 a a. Predictors: (Constant), BATHS, SQUAREFO, BEDROOMS b. Dependent Variable: ASKINGPR Regression Residual Total ANOVA b Sum of Squares df Mean Square F Sig a a. Predictors: (Constant), BATHS, SQUAREFO, BEDROOMS b. Dependent Variable: ASKINGPR Page

5 Coefficients a (Constant) SQUAREFO BEDROOMS BATHS Unstandardized Standardized Coefficients Coefficients B Std. Error Beta t Sig Page 2

6 Coefficients a (Constant) SQUAREFO BEDROOMS BATHS a. Dependent Variable: ASKINGPR Collinearity Statistics Tolerance VIF Collinearity Diagnostics a Dimension a. Dependent Variable: ASKINGPR Condition Variance Proportions Eigenvalue Index (Constant) SQUAREFO BEDROOMS BATHS Predicted Value Std. Predicted Value Standard Error of Predicted Value Adjusted Predicted Value Residual Std. Residual Stud. Residual Deleted Residual Stud. Deleted Residual Mahal. Distance Cook's Distance Centered Leverage Value a. Dependent Variable: ASKINGPR Residuals Statistics a Minimum Maximum Mean Std. Deviation N Charts Page 3

7 Histogram Dependent Variable: ASKINGPR Frequency 0 Std. Dev =.87 Mean = 0.00 N = Regression Standardized Residual.00 Normal P-P Plot of Regression Stan Dependent Variable: ASKINGPR.75 Expected Cum Prob Observed Cum Prob Page 4

8 Partial Regression Plot Dependent Variable: ASKINGPR ASKINGPR Rsq = SQUAREFO Partial Regression Plot Dependent Variable: ASKINGPR ASKINGPR Rsq = BEDROOMS Page 5

9 80 60 Partial Regression Plot Dependent Variable: ASKINGPR ASKINGPR Rsq = BATHS Regression Variables Entered/Removed a Variables Entered SQUAREF O Variables Removed a. Dependent Variable: ASKINGPR. Method Stepwise (Criteria: Probability -of-f-to-en ter <=.050, Probability -of-f-to-re move >=.00). Summary b R R Square Adjusted R Square Std. Error of the Estimate.749 a a. Predictors: (Constant), SQUAREFO b. Dependent Variable: ASKINGPR Page 6

10 Regression Residual Total a. Predictors: (Constant), SQUAREFO b. Dependent Variable: ASKINGPR ANOVA b Sum of Squares df Mean Square F Sig a Coefficients a (Constant) SQUAREFO Unstandardized Standardized Coefficients Coefficients B Std. Error Beta t Sig Page 7

11 Coefficients a Collinearity Statistics Tolerance VIF (Constant) SQUAREFO a. Dependent Variable: ASKINGPR Excluded Variables b BEDROOMS BATHS Partial Beta In t Sig. Correlation.387 a a Page 8

12 Excluded Variables b Collinearity Statistics Minimum Tolerance VIF Tolerance BEDROOMS BATHS a. Predictors in the : (Constant), SQUAREFO b. Dependent Variable: ASKINGPR Collinearity Diagnostics a Condition Variance Proportions Dimension Eigenvalue Index (Constant) SQUAREFO a. Dependent Variable: ASKINGPR Predicted Value Std. Predicted Value Standard Error of Predicted Value Adjusted Predicted Value Residual Std. Residual Stud. Residual Deleted Residual Stud. Deleted Residual Mahal. Distance Cook's Distance Centered Leverage Value a. Dependent Variable: ASKINGPR Residuals Statistics a Minimum Maximum Mean Std. Deviation N Charts Page 9

13 Histogram Dependent Variable: ASKINGPR Frequency Std. Dev =.96 Mean = 0.00 N = Regression Standardized Residual.00 Normal P-P Plot of Regression Stan Dependent Variable: ASKINGPR.75 Expected Cum Prob Observed Cum Prob Page 0

14 Stat 543 HW#4. Worried about Retirement? In February 2008, the Gallup organization surveyed,034 adults between 30 and 64 years of age and found that 548 were worried that they will outlive their money after they retire. Does the sample evidence suggest that a majority of 30- to 64-year-olds in the United States are worried they will outlive their money? Use the a = 0.05 level of significance. 7. Abstain from Alcohol In November 945, the Gallup organization surveyed,00 adult Americans and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?" Of the,00 adults surveyed, 363 indicated that they were total abstainers. In July 2007, the same question was asked of,00 adult Americans and 396 indicated that they were total abstainers. Has the proportion of adult Americans who totally abstain from alcohol changed? Use the a = 0.05 level of significance.

15 6. Rat's Hemoglobin Hemoglobin helps the red blood cells transport oxygen and remove carbon dioxide. Researchers at NASA wanted to determine the effects of space flight on a rat's hemoglobin. The following data represent the hemoglobin (in grams per deciliter) at lift-off minus 3 days (H-L3) and immediately upon the return (H-RO) for 2 randomly selected rats sent to space on the Spacelab Sciences flight. Rat S 6 H-L3,X H-RO, Y; Rat H-L3, X; _... ~ _, , H-RO, Y Source: NASA Life Sciences Data Archive Does the evidence suggest that the hemoglobin levels at lift-off minus 3 days are less than the hemoglobin levels upon return at the a = 0.05 level of significance? Note: A normal probability plot and boxplot of the.data indicate that the differences are approximately normally distributed with no outliers.

16 3. Concrete Strength An engineer wanted to know whether the strength of two different concrete mix designs differed significantly. He randomly selected 9 cylinders, measuring 6 inches in diameter and 2 inches in height, into which mixture was poured. After 28 days, he measured the strength (in pounds per square inch) of the cylinder. He also ral}domly selected 0 cylinders of mixture and performed the same test. The results are as follows: ~ixturc l\jixturc ,960 4,090 3,00 4,070 4,890 ~,020 4, , ,830 3,200 3,780 4,640 5,220.,.4,90 3, ,080 4,040 2,940 4,20 4,620. Note: Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers. Determine whether mixture is stronger than mixture at the a = 0.05 level of significance.