Please don\'t forget that there are FOUR parts to this question. A-D. 2. [6] Thr
ID: 3309248 • Letter: P
Question
Please don't forget that there are FOUR parts to this question. A-D.
2. [6] Throughout the semester we have been working with the real estate data from the Old Town neighborhood of Ames, Iowa. We can run a linear regression command in Rusing living_area as the explanatory variable and sale_price as the response variable. Summary output from R is shown below. (Note: I removed one outlier from the data set before running the regression command below.) Call: Im(formula = sale_price - living_area, data = old_town) Residuals: Min 19 Median 30 Max -82019 -14070 2038 16871 99621 Coefficients: Estimate std. Error t value Pr (>|t|) (Intercept) 32477.993 7466. 244 4.35 2.53e-05 *** living_area 41.278 3.298 12.52Explanation / Answer
a. equation of regression line :
sale price = 32477.993 + 41.278 * Living Area
b. H0 : = 0
Ha : 0
Test statistic
t = ^/ se = 41.278/ 3.298 = 12.52
Degree of freedom = 147
p - value = 2 x 10-16
so we can reject the null hypothesis as p - value is less than significance level so we conclude that sales price is associated with the living area.
(c) 95% confidence interval for = ^ +- tcr se0
critical value of t for alpha = 0.05 and dF = 147
tcr = 1.9762
= 41.278 +- 1.9762 * 3.298
= (34.76, 47.80)
(d) Here requirement of fitting a regression line are
(i) Homoscedasticity of residuals or equal variance : here we can see the residual plot that the residuals are random shown around the fitted line and on about near equal distance from the fitted line so yes it follows Homoscedasticity of residuals.
(ii) No autocorrelation of residuals : that can be interpreted when there is a relaton between residuals but it is not visible in given graph, as we can see its randomness.
(iiii) No perfect multicollinearity: single independent variable so yes no multicollinearity
(iv) Normality of residuals around 0.Which is satisfied by the linear regression line.