For a particular regression analysis, SST = 199.4082 and SSR = 188.9481. a. Obtain the coefficient of determination. b. Determine SSE.
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Olympic 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?For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy
- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.
- The following estimated regression equation based on 10 observations was presented. ŷ = 29.1260 + 0.5306x1 + 0.4680x2 The values of SST and SSR are 6,728.125 and 6,215.375, respectively. (a) Find SSE. SSE = (b) Compute R2. (Round your answer to three decimal places.) R2 = (c) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (d) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation.The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,801 and 1,758, respectively. (a)Compute R2. (Round your answer to three decimal places.) R2 = (b)Compute Ra2.(Round your answer to three decimal places.) Ra2 = (c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation.The estimated regression equation provided a good fit as a…The following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,807 and 1,757, respectively. (a) Compute R2. (Round your answer to three decimal places.) R2 = (b) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (c) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. The estimated regression equation did not provide a good…
- Which of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSyWhich of the following expressions is the correct way to express an interpretation for an OLS regression coefficient of -0.9? - This question is based on Data Analysis A. For every one unit increase in X there is - on average - a 0.9 unit decrease in Y. B. For every one unit increase in Y there is - on average - a 0.9 unit decrease in X. C. For every one unit increase in Y there is - on average - a 0.9 unit increase in X. D. For every one unit increase in X there is - on average - a 0.9 unit increase in Y.The following estimated regression equation based on 10 observations was presented. ŷ = 29.1670 + 0.5902x1 + 0.4960x2 Here, SST = 6,734.125, SSR = 6,212.375, sb1 = 0.0816, and sb2 = 0.0569. (a) Compute MSR and MSE. (Round your answers to three decimal places.) MSR=?? MSE=?? (b) Compute F and perform the appropriate F test. Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 = ?2 = 0 Ha: One or more of the parameters is not equal to zero. H0: ?1 > ?2 Ha: ?1 ≤ ?2 H0: ?1 ≠ 0 and ?2 ≠ 0 Ha: One or more of the parameters is equal to zero. H0: ?1 < ?2 Ha: ?1 ≥ ?2 H0: ?1 ≠ 0 and ?2 = 0 Ha: ?1 = 0 and ?2 ≠ 0 Find the value of the test statistic. (Round your answer to two decimal places.) F = ?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Reject H0. There is sufficient evidence to conclude that the overall model is significant. -Do not reject H0.…
