Regression Analysis: Selling price versus House size450 500 550-1000100Fitted ValueResidualResiduals Versus the Fitted ValuesQuiz 7 Name ANSWER KEYStat 217FORMULAS: 2nDFE DFSSMS  SSTSSMr 2A real estate expert was interested in developing a regression model that relates the selling price of a house (in thousands of dollars) to the house size (in square feet). Data were available on 30 properties that were recently sold.Regression Analysis: Selling price versus House sizeThe regression equation isSelling price = 316 + 0.0676 House sizePredictor Coef SE Coef T PConstant 315.74 46.98 6.72 0.000House size 0.06764 0.01593 4.25 0.000S = ***** R-Sq = ****% R-Sq(adj) = 37.0%Analysis of VarianceSource DF SS MS F PRegression ** 36282 36283 **** 0.000Residual Error ** 56359 ***** Total 29 926411. Fill the following blanks to complete the ANOVA table above. SHOW YOUR WORK! DFE = n-2 = 28 MSE = SSE/DFE = 56359/28 = 2012.822. Calculate R2 ?R2 = SSM/SST = 36282/92641 = .3916 ~ 39.2%3. Interpret the value of R2 39.2% of the variability of the house selling prices is explained by the line.4. What is the correlation between a house’s selling price and its size ? SHOW YOUR WORK!6258.3916. r 5. Is there sufficient evidence to suggest that the slope, 1, of the regression line is non-zero? From the regression output above, give:- the value of the test statistic - the distribution of the test statistic- the p-value which support your answer.Since the test statistic is t=4.25, t~t(28), then p-value=0.000, and we conclude that 01.6. Does the evidence suggest that there is a linear relationship between house size and selling price? Explain how you decided Yes or No. Since we concluded that 01, then the evidence does suggest that there is a linear relationship between house size and selling price.7. Use the regression line to estimate the selling price of a 2000 square foot house. SHOW YOUR WORK!!316 + .0676(2000) = 451.2. Thus, we estimate that the selling price for a 2000 square foot house is $451,200.8. Which TWO regression assumptions can you check using the Residual versus Fitted value plot at right? Does it appear that the these assumptions are satisfied for these data? Why or why not?The CONSTANT VARIANCE assumption appears to be met since the points are spread uniformly about the line. The LINEARITY assumption appears to be met since there is no pattern.9. Interpret the slope of the least squares regression line, b1 .b1 = .06764. Thus, for each additional square foot, the selling price of a house increases on average by $67.64.10. Which of the following is NOT an assumption for the simple linear regression model?A. There is a linear relationship between x and y.B. The mean of the yi’s is iyx10.C. The response variable y is normally distributed for each x.D. The explanatory variable x is normally distributed.11. For the least squares regression line, E. SSE is the smallest when compared to all other lines fit to the dataF. SSE is the largest when compared to all other lines fit to the dataG. SSE is the same when compared to all other lines fit to the