Based on the data shown below, calculate the regression line. y 1 44.75 2 43.56 40.27 4 34.98 33.19 30.7 7 27.21 8 25.32 22.23 10 21.54 11 16.15 12 14.56 13 12.77 14 8.78 15 5.69 16 4.5 y = X + [three decimal accuracy] [three decimal accuracy]
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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?Based on the results of the regression, what would be the mose likely conclusion?(1) Write out the regression equation (2) What is the sample size used in this investigation? (3) Determine the values of *, ** and ***, ****
- If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97Given the partial results from a linear regression model below, a sample size of 504, and ɑ=0.05, What is the F-Statistic for the overall model? Is it statistically significant? What is the R2 for the regression model above?Given the following, determine the price of a Corolla that is six years old given the graph of the regression line.
- BASED ON THIS DATA, what does the r^2 values tell you? and the linear regression line is the information statistically significant?Consider the following sample regression equation yˆ = 150 − 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). The slope coefficient indicates that if _____41. Which of the following is the multiple regression model for the data? (a) y = -0.11050 + 2.10797x1 + 0.40717x2 (b) y = -0.11050 + 0.40717x1 + 2.10797x2 (c) y = 0.23563 + 0.00062x1 + 0.23626x2 (d) none (e) y = -0.44187 + 2.42120x1 + 0.36135x2
- Use the sample linear regression line Y^=2+3X for the data points below to answer the following questions. X 0 3 7 10 Y 5 5 27 31 1) What is the fitted value when X2=3? 2) What is the regression residual when X2=3?Assume we have a population data, and the following values were obtained Mean of X=6, Standard deviation =2 Mean of Y = 11, standard deviation =3 R=-0.4. What is the slope and intercept of the regression line?Write the formula for the estimated regression line and interpret the slope of the estimated regression line, the intercept of the estimated regression line- Is it meaningful?, and the estimated R2. Based on the fitted regression model, what is the predicted ATST for a child who is 7 years old? What is the correlation between AGE and ATST? Does the residual plot suggest that the fitted regression line is inappropriate for these data? Explain why or why not. Suppose that a new subject is added to the study data and that subject is 12.5 years old with an ATST of 580 minutes. If the regression model were to be refit with this additional data point, would the new slope be greater than or less than -14.041? Justify your response.