What exactly is homoscedasticity
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What exactly is homoscedasticity?
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- Please see picture and answer questions A and B (a)Which city had the highest noon temperature? Choose one (City A/ City b/ Both had the highest) (b)Which city had noon temperatures with a larger interquartile range (IQR)? Choose one (City A/ City B/ Both had the same IQR)When a group of subjects entered a room, researchers recorded both the color of shirt worn by thesubject, and whether or not the subject smiled. The results are recorded below. With 0.05significance, test the claim that color of shirt and smiling are independent. Use your calculator.Smiled No SmileGreen Shirt 15 10Blue Shirt 13 7Yellow Shirt 5 8In a business, the Chief Executive Officer wants to know if his workers are for or against mandatory vaccinations. A random sample of 200 workers was taken and the results are shown in the MINITAB output below Expected counts are printed below observed counts Managers Team leaders Employees Total 17 22 15 Approve 21.330 17.820 14.850 54 34 25 14 Against 28.835 24.090 20.075 73 28 19 26 No Opinion 28.835 24.090 20.075 73 Total 79 66 55 200 Chi-sq = 0.878992 + 0.980494 + 0.001515 + 0.925168+ 0.034375 + 1.838387 + 0.02418 + 1.075471 + 1.74874 =7.507306
- In the following plot you see the rejection frequencies (defined as the frequency in which the estimator is non-zero) for 100 regressors (represented along the horizontal axis), and repeated for the OLS, Lasso and Adaptive Lasso estimators. The red dots are the estimates for the true non-zero coefficients. The black dots are the estimates of true-zero coefficients. OLS Lasso Adaptive Lasso 12- 12- 1.2- 0.8- 0.8- 0.8- 0.4- 0.4- 0.4- 0.0- 0.0- 0.0- 100 100 You can learn from the plots that: O a. The Lasso has a clear shrinkage towards zero O b. The Adaptive Lasso has better model-selection properties because it estimates more frequently the true zeros as zeros O. All of the options Od. The OLS has poor predictive performance O e. The Adaptive Lasso has better model-selection properties because it estimates more frequently the true non-zeros as non-zeros coef *8-Suppose the following information is known P[A] = 0.8, P[B] = 0.5, P[A and B] = 0.40. The values for P[B|A] and P[A|B] are respectively: (a) It cannot be determined. (b) 0.65, 0.75 (c) 0.65, 0.70 (d) 0.50, 0.80 (e) 0.50, 0.75As suburban gardeners know, deer will eat almost anything green. In a study of pine seedlings at an environmental center in Ohio, researchers noted how deer damage varied with how much of the seedling was covered by thorny undergrowth. Deer damage Deer damage Thorny cover Yes No None 6060 151151 <13<13 7676 158158 1313 to 2323 4444 177177 >23>23 2929 176176 (a) What is the probability that a randomly selected seedling was damaged by deer? (Enter your answer rounded to two decimal places.) probability = (b) What are the conditional probabilities that a randomly selected seedling was damaged, given each level of cover? (?= a seedling was damaged by a deerD= a seedling was damaged by a deer .) Drag the correct answer to the appropriate column. ?(? | P(D | no cover))?(? | cover <13)P(D | cover <13)?(? |13 ?? 23)P(D |13 to 23)?(? | cover>23)
- The contingency table to the right shows counts of the types of gasoline bought during the week and during weekends. (a) Find the value of chi-squared and Cramer's V for this table. (b) Interpret these values. What do these tell you about the association in the table? (a) x² = (Round to two decimal places as needed.) Premium Plus Regular Total Weekday Weekend Total 124 124 248 96 194 290 469 106 689 424 575 1113 nFor the chi-square test of independence, Provide a hypothetical formulation of test of independence.What degrees of freedom would younormally expect a t test to have when N1 = 40 and N2 = 55?