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Aplia: Student Question Fill In The Blanks. I Cheg V(2) Corny Jim's Ring S 4X × X C courses aplia.com/af/ser let/quiz?quiz actiontakeQuiz&quiz; probGuid-QNAPC0A801010000003b8d7620060000&ctx;=delil martinez-0003&ckzm; 151 1238344602 0AAA6B0. @) aplia Applied Statistics for Business and Economics F17 Customer Support T Sign Out Michael Norton Home Grades Discussion Course Materials Multiple Regression Graded Assignment | Read Chapter 15 | Back to Assignment Due Sunday 12.10.17 at 11:45 PM Average: /9 Attempts: 3. Model assumptions In a multiple regression model with p independent variables, that is, y-Po 1X1 + + pxp + e, you have the following assumptions. Assumption 1: The error term is a random variable with a mean of zero; that is, E(E) = 0 for all values of the independent variables x. Assumption 2: The variance of E, denoted by 2, is the same for all values of the independent variables xi, X2, , Xp. Assumption 3: The values of are independent. Assumption 4: The error term is a normally distributed random variable. The residuals plotted against Y, the predicted value of y, can be used to validate the assumptions of the multiple regression model. The error term E is the difference betweern The residual is the difference between , assuming that the regression model is true. The is an approximation of the Session 5928 Timeout 8:26 PM 11/20/2017Explanation / Answer
The error term e is the difference between the observed value and the unobservable true value of a quantity eg, a population mean.
Residual is the difference between the observed value and the estimated value of the quantity eg, a sample mean.
Residual is an approximation of the error E, assuming the regression is true.
Figure1
The assumption 1 seems to be violated, the mean of error terms is not same for all independent values of x.
Figure 2
The assumption 1 seems to be violated, the mean of error terms is not same for all independent values of x. Mean is positive first then it goes negative and then positive again. This shows that the model fitted is not a perfect fit, and there is a serious issue with the regression model.
Figure 3
The assumption 2 is violated, the variance is small in the beginning but it goes on increasing until the end.
Figure 4
None of the choices is correct. The residuals are centred at 0 and variance is also equal for independent values of x.
Figure 5 Histogram.
Assumption 4 is violated. Residual are not normally distributed.
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