Based image, explain the table in one paragraph.
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1. Based image, explain the table in one paragraph.
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Which of the following is/are true if the coefficient of determination between the response and the predictor variables is 81 percent based on a random sample of size n i. the pearson's sample correlation coefficient is +0.9 ii. this means that 19 percent of the total variation in the response variable remains unexplained by tge simple linear regression model that uses the given predictor variable iii both i and ii iv neither i and iia. Compute the correlation between price and mileage. (Round answers to 4 decimal points) Correlation: b. Which of the following is NOT an assumption made on the standard regression assumptions? Which of the following is true about the regression line multiple choice 2 The regression line minimizes the MSE of forecast errors. The regression line is the line with the largest prediction accuracy. The regression line minimizes the sum of the squares of the residuals. Regression may only be performed if the standard regression assumptions hold. All of the above. multiple choice 1 They all follow a binomial distribution They are all independent of each other They all have the same standard deviation They all have mean (expected value) 0
- (A) What do you understand by the term ‘autocorrelation’?(e) An econometrician suspects that the residuals of her model might be autocorrelated. Explain the steps involved in testing this theory using the Durbin–Watson (DW) test.Consider the regression model Y = B0 + B1 X1 + B2 X2 + u. Suppose you want to test the null hypothesis H0: B1 + B2 = 0, versus the alternative hypothesis H1: B1+ B2 != 0 (!= means "not equal to"). The data set consists of 100 observations. (a) Suppose we use an F-statistic to conduct the test. What are the degrees of freedom associated with this test statistic? (b) Let G(.) be the CDF of the F-distribution for the F-statistic in part (b). Denote the actual F-statistic by F_act. Suppose someone says that you should reject the null at the 5% significance level if G(F_act)<0.05. Explain whether you agree with this approach. (c) Suppose you find that the F-test in part (b)-(c) and the test in part (a) yield very different p-values. Do you think this result is correct? Briefly explain your reasoning.9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. a) What is heteroscedasticity? (b) Why is heteroscedasticity a problem? c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).
- Which of the following statements is/are correct about logistic regression? Logistic regression can be used for modeling the continuous response variable with dichotomous explanatory variable. Logistic regression can be used for modeling the dichotomous response variable with dichotomous explanatory variable. Logistic regression can be used for modeling the continuous response variable with dichotomous or other type of categorical explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with dichotomous and not for continuous explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with categorical explanatory variables and/or continuous explanatory variables.Which of the following statements about a least-squares regression analysis is true?I. A point with a large residual is an outlier.II. A point with high leverage has a -value that is not consistent with the other -values in the set.III. The removal of an influential point from a data set could change the value of the correlation coefficient.15.3 #6 The authors of the article "Age, Spacing and Growth Rate of Tamarix as an Indication of Lake Boundary Fluctuations at Sebkhet Kelbia, Tunisia"† used a simple linear regression model to describe the relationship between y = vigor (average width in centimeters of the last two annual rings) and x = stem density (stems/m2). The estimated model was based on the following data. Also given are the standardized residuals. x 4 5 6 9 14 15 15 19 21 22 y 0.75 1.20 0.55 0.60 0.65 0.55 0.00 0.35 0.45 0.40 Std resid −0.28 1.92 −0.90 −0.28 0.54 0.24 −2.05 −0.12 0.60 0.52 Are there any points with unusually large residuals? (Select all that apply.) A) (x, y) = (4, 0.75) B) (x, y) = (15, 0.00) C) (x, y) = (14, 0.65) D) (x, y) = (5, 1.20) E) (x, y) = (15, 0.55) F) (x, y) = (9, 0.60) G) (x, y) = (6, 0.55) H) none of the above
- 15.3 #6 The authors of the article "Age, Spacing and Growth Rate of Tamarix as an Indication of Lake Boundary Fluctuations at Sebkhet Kelbia, Tunisia"† used a simple linear regression model to describe the relationship between y = vigor (average width in centimeters of the last two annual rings) and x = stem density (stems/m2). The estimated model was based on the following data. Also given are the standardized residuals. x 4 5 6 9 14 15 15 19 21 22 y 0.75 1.20 0.55 0.60 0.65 0.55 0.00 0.35 0.45 0.40 Std resid −0.28 1.92 −0.90 −0.28 0.54 0.24 −2.05 −0.12 0.60 0.52 (a) What assumptions are required for the simple linear regression model to be appropriate? (Select all that apply.) A) The random errors associated with different observations are dependent on one another. B) The distribution of e at any given x is not normal. C) The distribution of e at any given x is normal. D) The distribution of e at any particular x value has mean value 0. E) The random…Answer true or false to the following statements and explain your answers. a. In multiple linear regression, we can determine whether we are extrapolating in predicting the value of the response variable for a given set of predictor variable values by determining whether each predictor variable value falls in the range of observed values of that predictor. b. Irregularly shaped regions of the values of predictor variables are easy to detect with two-dimensional scatterplots of pairs of predictor variables, and thus it is easy to determine whether we are extrapolating when predicting the response variable.
