In order to help clients determine the price at which their house is likely to sell,...

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In order to help clients determine the price at which their house is likely to sell, a realtor gathered a sample of 30 purchase transactions in her area during a recent three-month period. For the response of the model, use the price of the home (in thousands of dollars). As explanatory variables, use the number of square feet (also in thousands) and the number of bathrooms. Complete parts a through f. Click the icon to view the data table. ... (a) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the responses. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression? Examine the scatterplot to the right. Are there any unusual features in the data? A. The scatterplot plot shows an unusual correlation. B. The scatterplot does not have any unusual features. C. The scatterplot does not correctly plot the data. 'D. The scatterplot has leveraged outliers that should be investigated. Price ($000's) 881- Q 496- 111 1 3 5 7 9 11 Sq Feet (thousands) Examine the scatterplot to the right. Are there any unusual features in the data? A. The scatterplot plot shows an unusual correlation. B. The scatterplot does not correctly plot the data. 'C. The scatterplot has leveraged outliers that should be investigated. D. The scatterplot does not have any unusual features. Price ($000's) 881- 496- 111 1 2 3 4 Bathrooms Examine the scatterplot to the right. Are there any unusual features in the data? A. The scatterplot plot shows an unusual correlation. 'B. The scatterplot has leveraged outliers that should be investigated. C. The scatterplot does not correctly plot the data. D. The scatterplot does not have any unusual features. Bathrooms 5- 4- 2 ... 1 3 5 7 a 11 Do the relevant plots appear straight enough for multiple regression? 'A. The scatterplots have leveraged outliers. The association appears linear and the two explanatory variables are correlated. B. The scatterplots do not have any unusual features. C. The scatterplots appear straight, but not straight enough for multiple regression. D. The scatterplots all appear to have no correlation. (b) Fit the multiple regression and show a summary of the estimated features of the model. Complete the table below. (Round R and so to three decimal places. Round all coefficients and standard errors to one decimal place. Round all test statistics to two decimal places. Round all probabilities to three decimal places.) R Se 0.466 132.048 Term Intercept Estimate Std Error t Ratio Prob > 85.8 61.4 1.40 0.174 Sq Feet 27.2 11.3 2.39 0.024 Bathrooms 57.7 24.7 2.33 0.027 |t|| (c) Does the fitted model appear to meet the conditions for the use of the multiple regression model (MRM)? Choose the correct answer below. A. No, the residuals are not nearly normal. B. No, there are a substantial amount of lurking variables that have not been considered. C. Yes, although there is concern over the effect of the leveraged outliers. D. No, there are too many outliers. The data is not normal. What are the null and alternative hypotheses? = 0 A. Ho B =B2= HA: B1B2>0 C. Ho B10 or #0 HA B =B2=0 Find the F-statistic. F = 11.8 B. Ho: B =B2=0 HA B0 or B2 0 D. Ho B =2=0 HA: B1 (Type an integer or decimal rounded to one decimal place as needed.) Find the p-value. p = 0.000 (Round to three decimal places as needed.) Determine a conclusion using a level of significance of 0.05. A. Reject the null hypothesis. The p-value is not smaller than needed to assure statistical significance. B. Reject the null hypothesis. The p-value is smaller than needed to assure statistical significance. C. Fail to reject the null hypothesis. The p-value is not smaller than needed to assure statistical significance. D. Fail to reject the null hypothesis. The p-value is smaller than needed to assure statistical significance. (e) Compare the marginal slope for the number of bathrooms to the partial slope. Explain why these are so different, and show confidence intervals for each. (Use a 95% confidence interval.) The 95% confidence interval for the marginal slope is about $ to $ (Round to the nearest thousand dollars as needed.) per bathroom. In order to help clients determine the price at which their house is likely to sell, a realtor gathered a sample of 30 purchase transactions in her area during a recent three-month period. For the response of the model, use the price of the home (in thousands of dollars). As explanatory variables, use the number of square feet (also in thousands) and the number of bathrooms. Complete parts a through f. Click the icon to view the data table. ... (a) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the responses. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression? Examine the scatterplot to the right. Are there any unusual features in the data? A. The scatterplot plot shows an unusual correlation. B. The scatterplot does not have any unusual features. C. The scatterplot does not correctly plot the data. 'D. The scatterplot has leveraged outliers that should be investigated. Price ($000's) 881- Q 496- 111 1 3 5 7 9 11 Sq Feet (thousands) Examine the scatterplot to the right. Are there any unusual features in the data? A. The scatterplot plot shows an unusual correlation. B. The scatterplot does not correctly plot the data. 'C. The scatterplot has leveraged outliers that should be investigated. D. The scatterplot does not have any unusual features. Price ($000's) 881- 496- 111 1 2 3 4 Bathrooms Examine the scatterplot to the right. Are there any unusual features in the data? A. The scatterplot plot shows an unusual correlation. 'B. The scatterplot has leveraged outliers that should be investigated. C. The scatterplot does not correctly plot the data. D. The scatterplot does not have any unusual features. Bathrooms 5- 4- 2 ... 1 3 5 7 a 11 Do the relevant plots appear straight enough for multiple regression? 'A. The scatterplots have leveraged outliers. The association appears linear and the two explanatory variables are correlated. B. The scatterplots do not have any unusual features. C. The scatterplots appear straight, but not straight enough for multiple regression. D. The scatterplots all appear to have no correlation. (b) Fit the multiple regression and show a summary of the estimated features of the model. Complete the table below. (Round R and so to three decimal places. Round all coefficients and standard errors to one decimal place. Round all test statistics to two decimal places. Round all probabilities to three decimal places.) R Se 0.466 132.048 Term Intercept Estimate Std Error t Ratio Prob > 85.8 61.4 1.40 0.174 Sq Feet 27.2 11.3 2.39 0.024 Bathrooms 57.7 24.7 2.33 0.027 |t|| (c) Does the fitted model appear to meet the conditions for the use of the multiple regression model (MRM)? Choose the correct answer below. A. No, the residuals are not nearly normal. B. No, there are a substantial amount of lurking variables that have not been considered. C. Yes, although there is concern over the effect of the leveraged outliers. D. No, there are too many outliers. The data is not normal. What are the null and alternative hypotheses? = 0 A. Ho B =B2= HA: B1B2>0 C. Ho B10 or #0 HA B =B2=0 Find the F-statistic. F = 11.8 B. Ho: B =B2=0 HA B0 or B2 0 D. Ho B =2=0 HA: B1 (Type an integer or decimal rounded to one decimal place as needed.) Find the p-value. p = 0.000 (Round to three decimal places as needed.) Determine a conclusion using a level of significance of 0.05. A. Reject the null hypothesis. The p-value is not smaller than needed to assure statistical significance. B. Reject the null hypothesis. The p-value is smaller than needed to assure statistical significance. C. Fail to reject the null hypothesis. The p-value is not smaller than needed to assure statistical significance. D. Fail to reject the null hypothesis. The p-value is smaller than needed to assure statistical significance. (e) Compare the marginal slope for the number of bathrooms to the partial slope. Explain why these are so different, and show confidence intervals for each. (Use a 95% confidence interval.) The 95% confidence interval for the marginal slope is about $ to $ (Round to the nearest thousand dollars as needed.) per bathroom.