4. Comment on each of the following statements: 1) Standard residuals are used to catch outliers in the predictor variable. 2) Standard residuals are obtained by multiplying the residuals by root of MSE. 3) The residual plot is the only tool that shows the linearity or non-linearity of the regression relation.
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- Assume we have data demonstrating a strong linear link between the amount of fertilizer applied to certain plants and their yield. Which is the independent variable in this research question?To evaluate whether the assumption of linearity has been violated, which of the following graph should be examined? A. QQ plot of residuals B. Predicted Values vs. Residuals C. Residuals vs. Progrm Per-Year Tuition ($) D. Residual index plot b) To evaluate whether the assumption of normality has been violated, which of the following graph should be examined? A. Predicted Values vs. Residuals B. Residuals vs. Progrm Per-Year Tuition ($) C. Residual index plot D. QQ plot of residuals c) To evaluate whether the assumption of equal variance has been violated, which of the following graph should be examined? A. Predicted Values vs. Residuals B. Residual index plot C. Residuals vs. Progrm Per-Year Tuition ($) D. QQ plot of residuals d) To evaluate whether the assumption of independence has been violated, which of the folowing graph should be examined? A. Residual index plot…A researcher is surprised at the low Pearson Product Moment correlation coefficient between the heights and weights of the members of the woman’s basketball team at his college. He should have realized a. that he had several outliers and that reduced the correlation b. the range of heights was restricted and that reduced the correlation c. the relationship was curvilinear and could not be detected by the Pearson Product Moment correlation d. Height does not cause weight
- It is known that a natural law obeys the quadratic relationship y = ax-. Whatis the best line of the form y = px + q that can be used to model data and minimize Mean-Squared-Error if all of the data points are drawn uniformly atrandom from the domain [0, 1]?2. A scatterplot shows a strong, positive, linear relationship between the number of rebounds a basketball team averages and the number of wins that team records in a season. Which conclusion is most appropriate? (A) A team that increases its number of rebounds causes its chances of winning more games to increase. (B) If the residual plot shows no pattern, then it is safe to conclude that getting more rebounds causes more wins, on average. (C) If the residual plot shows no pattern, then it is safe to conclude that getting more wins causes more rebounds, on average. (D) If the r^2r2 value is close enough to 100%, then it is safe to conclude that getting more rebounds causes more wins, on average. (E) Rebounds and wins are positively correlated, but we cannot conclude that getting more rebounds causes more wins, on average.The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: a) Are the estimates ˆa ,ˆb , and cˆ statistically significant at the 2 percent level of significance? Which is/are significant and which is/are not? b) Do the results indicate that the average variable cost curve is ∪-shaped? How do you know?c) If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost? Marginal cost? Total variable cost? Total cost? d) Answer part c, assuming that Argus produces 10,000 vacuum cleaners monthly. e) at what level of output will average variable cost be at a minimum? What is the minimum average variable cost?
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