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3. (No R required) Recall that fitted values and residuals from the fitted regression line are...
Question 14 Below is a residual plot of a regression model. Residuals Versus the Fitted Values...
Question 14 Below is a residual plot of a regression model. Residuals Versus the Fitted Values (response is RETURN) 4 1 3 T 1 Standardized Residual 0 -2 -3 10 20 30 Fitted Value The above plot indicates o (a) an incorrect specification of the model. o (b) a clear violation of homoscedasticity. o (c) a high correlation among the residuals. (d) the existence of an outlier o (a) and (b) o (a) and (c) o (b) and (c) o...
3. Prove that the sample covariance between the fitted values and the residuals ûi is always...
3. Prove that the sample covariance between the fitted values and the residuals ûi is always zero in the simple linear regression model with an intercept. Show all of the steps in your derivation.
The results shown below provide the X-values, residuals, and a residual plot from a regression analysis....
The results shown below provide the X-values, residuals, and a residual plot from a regression analysis. Is there any evidence of a pattern in the residuals? Explain. X Residual 1 .79 2 -0.84 3 1.19 4 -0.38 5 2.36 6 -0.73 7 0.19 8 1.62 9 -1.15 10 1.77 Choose the correct answer below. A. Yes, the residuals show decreasing variation. B. No, the residuals appear to be randomly spread. C. Yes, the residuals show a distinct cyclical pattern. D....
Consider the following observed values: (-5,-2) (-3,1) (0,4) (2,6) (1,3) (1) find the estimated regression line...
Consider the following observed values: (-5,-2) (-3,1) (0,4) (2,6) (1,3) (1) find the estimated regression line based on the observed data (2) for each xi, compute fitted value of yi (3) compute the residuals ei (4) calculate the coefficient of determination
mealenk RI TAT Problem 2: ON Consider the tollowing observed values of (Ti, Yi): (2, –1)...
mealenk RI TAT Problem 2: ON Consider the tollowing observed values of (Ti, Yi): (2, –1) (0, 3), (1, 2), (-1,6), a. Find the estimated regression line ŷ = Bo + Bịa, based on the observed data. b. For each xi, compute the fitted value of 3Y; using c. Compute the residuals, e; = Yi-;- d. Find R-squared (the coefficient of determination). (a) (b) (c)
3. In the usual setup for multiple regression, e, hi, Vo) are the raw residual, leverage, and the...
3. In the usual setup for multiple regression, e, hi, Vo) are the raw residual, leverage, and the i-th leave-one-out fitted response, respectively. The i-th deleted residual sum of square is defined as where yo: (n-1)x1, the response vector with the i-th entry deleted; Xo): (n-1) x p is the design matrix with the i-th row deleted (a) (Stat438 ONLY) Show that SSRestSSRes-_ by using the following results SS Res e2 SSRes (b) Use the result from (a), show that...
please be detailed in your response :) thank you! 0 pts) You are given the following estimated equation: In(wage) 0.1279+0.0904educ + 0.041 exper-0 (0.1059) (0.0075) (0.0052) (0.00012) R 0.3003 5...
please be detailed in your response :) thank you!
0 pts) You are given the following estimated equation: In(wage) 0.1279+0.0904educ + 0.041 exper-0 (0.1059) (0.0075) (0.0052) (0.00012) R 0.3003 526 in which: log(wage) log of average hourly wage - educ is the number of years of schooling: - exper is the number of years of experience -exper'=experience"experience The plot of the residuals against the fitted values from the regression above, is provided below: .5 2.5 1.5 Fitted values a. With...
4. We have n statistical units. For unit i, we have (x; yi), for i 1,2,...,n. We used the least squares line to obtain the estimated regression line bobi . (a) Show that the centroid (z, y) is a poin...
4. We have n statistical units. For unit i, we have (x; yi), for i 1,2,...,n. We used the least squares line to obtain the estimated regression line bobi . (a) Show that the centroid (z, y) is a point on the least squares line, where x-(1/n) Σ-Χί and у-(1/ n) Σ|-1 yi. (Hint: Evaluate the line at x x.) (b) In the suggested exercises, we showed that e,-0 and where e is the ith residual, that is e -y...
Consider the following regression results: Describe how the response y depends on the regressor x. What...
Consider the following regression results:
Describe how the response y depends on the regressor x. What is
the formula for the regression line? What is the B0 and B1, and
what do these coefficients represent? The Residuals vs. fitted plot
is used to assess what assumption? What does the above plot tell
you about your data? (remember to round all answers to 3 decimal
places)
Call: Im(formula = y ~ X, data = d) Residuals: Min 1Q Median 3Q Max...
2. Suppose Y ~ Exp(a), which has pdf f(y)-1 exp(-y/a). (a) Use the following R code to generate data from the model Yi...
2. Suppose Y ~ Exp(a), which has pdf f(y)-1 exp(-y/a). (a) Use the following R code to generate data from the model Yi ~ Exp(0.05/Xi), and provide the scatterplot of Y against X set.seed(123) n <- 500 <-rnorm (n, x 3, 1) Y <- rexp(n, X) (b) Fit the model Yi-Ao + Ax, + ε¡ using the lm function in R and provide a plot of the best fit line on the scatterplot of Y vs X, and the residual...
Question 14 Below is a residual plot of a regression model. Residuals Versus the Fitted Values (response is RETURN) 4 1 3 T 1 Standardized Residual 0 -2 -3 10 20 30 Fitted Value The above plot indicates o (a) an incorrect specification of the model. o (b) a clear violation of homoscedasticity. o (c) a high correlation among the residuals. (d) the existence of an outlier o (a) and (b) o (a) and (c) o (b) and (c) o...
3. Prove that the sample covariance between the fitted values and the residuals ûi is always zero in the simple linear regression model with an intercept. Show all of the steps in your derivation.
mealenk RI TAT Problem 2: ON Consider the tollowing observed values of (Ti, Yi): (2, –1) (0, 3), (1, 2), (-1,6), a. Find the estimated regression line ŷ = Bo + Bịa, based on the observed data. b. For each xi, compute the fitted value of 3Y; using c. Compute the residuals, e; = Yi-;- d. Find R-squared (the coefficient of determination). (a) (b) (c)
3. In the usual setup for multiple regression, e, hi, Vo) are the raw residual, leverage, and the i-th leave-one-out fitted response, respectively. The i-th deleted residual sum of square is defined as where yo: (n-1)x1, the response vector with the i-th entry deleted; Xo): (n-1) x p is the design matrix with the i-th row deleted (a) (Stat438 ONLY) Show that SSRestSSRes-_ by using the following results SS Res e2 SSRes (b) Use the result from (a), show that...
please be detailed in your response :) thank you!
0 pts) You are given the following estimated equation: In(wage) 0.1279+0.0904educ + 0.041 exper-0 (0.1059) (0.0075) (0.0052) (0.00012) R 0.3003 526 in which: log(wage) log of average hourly wage - educ is the number of years of schooling: - exper is the number of years of experience -exper'=experience"experience The plot of the residuals against the fitted values from the regression above, is provided below: .5 2.5 1.5 Fitted values a. With...
4. We have n statistical units. For unit i, we have (x; yi), for i 1,2,...,n. We used the least squares line to obtain the estimated regression line bobi . (a) Show that the centroid (z, y) is a point on the least squares line, where x-(1/n) Σ-Χί and у-(1/ n) Σ|-1 yi. (Hint: Evaluate the line at x x.) (b) In the suggested exercises, we showed that e,-0 and where e is the ith residual, that is e -y...
Consider the following regression results:
Describe how the response y depends on the regressor x. What is
the formula for the regression line? What is the B0 and B1, and
what do these coefficients represent? The Residuals vs. fitted plot
is used to assess what assumption? What does the above plot tell
you about your data? (remember to round all answers to 3 decimal
places)
Call: Im(formula = y ~ X, data = d) Residuals: Min 1Q Median 3Q Max...
2. Suppose Y ~ Exp(a), which has pdf f(y)-1 exp(-y/a). (a) Use the following R code to generate data from the model Yi ~ Exp(0.05/Xi), and provide the scatterplot of Y against X set.seed(123) n <- 500 <-rnorm (n, x 3, 1) Y <- rexp(n, X) (b) Fit the model Yi-Ao + Ax, + ε¡ using the lm function in R and provide a plot of the best fit line on the scatterplot of Y vs X, and the residual...
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