1 . A home appraisal company would like to develop a regression…
QuestionAnswered step-by-step1 . A home appraisal company would like to develop a regression…1. A home appraisal company would like to develop a regression model that would predict the selling price of a house based on the age of the house in years (Age), the living area of the house in square feet (Living Area) and the number of bedrooms (Bedrooms). The following Excel output shows the partially completed regression output from a random sample of homes that have recently sold. What is the critical value to test the significance of the regression coefficients usingα=0.05?Round to three decimal places.Image transcription text- X Regression summary outputSUMMARY OUTPUT RegressionStatistics Multiple R 0.84… Show moreImage transcription textX Confidence interval estimate Confidence Interval Estimateand Prediction Interval Data Confidence Level 95% Age givenvalue 10 Living Area given value 2400 Bedrooms g… Show more A. 2.145B. 2.131C. 2.179D. 2.201 5. An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced in the accompanying tables. To test whether aggregate price index has a positive impact on consumption, what is the p-value?SUMMARY OUTPUTMultiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 df SS MS F Signif F Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat P-value Intercept −0.0861 0.5674 −0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price −0.0006 0.0028 −0.219 0.8330 A.0.4165B.0.0001C.0.5835D.0.8330 14. What can predict how much a motion picture will make? Data on a number of recent releases that includes the Gross ($M), the Budget ($M), the Run Time (minutes), and the average number of Stars awarded by reviewers was collected and a regression model was created to predict Gross. Use the computer output given below to complete parts a through e.Dependent variable is: GrossR squared=42.0%,R squared (adjusted)=40.5%s=46.39 with 120−4=116 degrees of freedomVariable Coef SE(Coef) t-ratio P-value Intercept −22.6229 25.69 −0.88 0.3807 Budget 1.14088 0.12318 9.26 0.0000 Stars 23.8671 5.968 4.00 0.0001 Run Time −0.419196 0.2461 −1.70 a) What is the null hypothesis tested for the coefficient of Run Time in this table? A. H0: βRun Time=0B. H0: βRun Time≠0C. H0: βRun Time>0D. H0: βRun Time<0 b) What is the t-statistic corresponding to this test? *I think I'm very unsure of how to find a t-statistic, because I'm stuck on every problem like this.enter your response here ________________ (integer or a decimal. Do not round.) c) Why is this t-statistic negative?The t-statistic is negative because the __ is __....▼ coefficientstandard error of the coefficientt-ratioP-value is ▼positive.negative.zero. d) What is the P-value corresponding to this t-statistic?enter your response here ___________ (integer or a decimal. Do not round.) e) Complete the hypothesis test usingα=0.05.Do you reject the null hypothesis? A. Reject H0. There is sufficient evidence that the coefficient of Run Time is different from 0.B. Fail to reject H0. There is sufficient evidence that the coefficient of Run Time is different from 0.C. Fail to reject H0. There is insufficient evidence that the coefficient of Run Time is different from 0.D. Reject H0. There is insufficient evidence that the coefficient of Run Time is different from 0. 15. Data were gathered from a simple random sample of cities. The variables are Violent Crime (crimes per 100,000 population), Police Officer Wage (mean $/hr), and Graduation Rate (%). Use the accompanying regression table to answer the following questions consider the coefficient of Graduation Rate. Complete parts a through e. Dependent variable is: Violent CrimeR squared=41.1%R squared (adjusted)=43.5%s=129.6 with 37 degrees of freedomVariable Coeff SE (Coeff) t-ratio P-value Intercept 1383.47 185.3 7.47 < 0.0001 Police Officer Wage 9.18 4.293 2.14 0.0392 Graduation Rate −16.28 2.400 −6.78 < 0.0001 a) State the standard null and alternative hypotheses for the true coefficient of Graduation Rate.A.H0:βGradRate=0HA:βGradRate<0B.H0:βGradRate≠0HA:βGradRate=0C.H0:βGradRate=0HA:βGradRate>0D.H0:βGradRate=0HA:βGradRate≠0 Part 2b) What is the t-statistic corresponding to this test? The t-statistic is enter your response here. _____________ (integer or a decimal.) Part 3c) Why is the t-statistic negative?A.The t-statistic is negative because R squared (adjusted) is less than 50%.B.The t-statistic is negative because the coefficient is negative.C.The t-statistic is negative because R squared is less than 50%.D.The t-statistic is negative because the coefficient has the smallest standard error. Part 4d) What is the P-value corresponding to this t-statistic?A.<0.0001B.−0.602C. 9.18D.0.0392 Part 5e) Test the null hypothesis (at α=0.05) and state your conclusion.A.Fail to reject H0. There is insufficient evidence that the coefficient is different from 0.B. Reject H0. There is sufficient evidence that the coefficient is different from 0.C.Fail to reject H0. There is sufficient evidence that the coefficient is different from 0.D.Reject H0. There is insufficient evidence that the coefficient is different from 0. 17. Use the accompanying regression table to answer the following questions. Complete parts (a) through (c).Data were gathered from a simple random sample of cities. The variables are Violent Crime (crimes per 100,000 population), Police Officer Wage (mean $/hr), and Graduation Rate (%).Dependent variable is: Violent CrimeR squared=38.7%R squared (adjusted)=40.9%s=129.6 with 37 degrees of freedomSource Sum of Squares df Mean Square F-ratio Regression 701686 2 350843 20.9 Residual 621046 37 16785 .0 Variable Coeff SE (Coeff) t-ratio P-value Intercept 1385.73 182.9 7.58 < 0.0001 Police Officer Wage 9.21 4.115 2.24 0.0313 Graduation Rate −16.48 2.500 −6.59 < 0.0001 a) How was the t-ratio of 2.24 computed for Police Officer Wage? (Show what is computed using numbers from the table.)A. 350843/ 16785.0B. 701686/ 621046C. 9.21/ 4.115D.1385.73/ 618.629E. 4.115/ 2.500F. 4.115/ 1.837 Part 2b) How many cities are used in this model? How do you know?A. 37, because the degrees of freedom is 37B. 38, because the degrees of freedom is 37, and that's equal to number of cases−1C. 39, because the degrees of freedom is 37, and that's equal to number of cases−number of predictor variablesD. 40, because the degrees of freedom is 37, and that's equal to number of cases−number of predictor variables−1 Part 3c) The t-ratio for Graduation Rate is negative. What does that mean?A.The t-ratio is negative because the coefficient is negative.B.As the graduation rate goes down, the average police officer wage goes up.C. The t-ratio is negative because as the graduation rate goes down, the violent crime rate increases. MathStatistics and ProbabilityBUSN 203Share Question
