Calculate for the coefficient b in the linear regression equation describing the sample data
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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?1a. Develop an estimated regression equation for these data. 1b. Compute the residuals and standardized residualsrandomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1.5 2 3 3.5 4 4.5 5.5 Overall Grades 99 96 84 75 68 65 60 Table Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places.
- randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1.5 2 3 3.5 4 4.5 5.5 Overall Grades 99 96 84 75 68 65 60 Table Find the estimated slope, y interscept and correlation coefficient Round your answers to three decimal places.14.Calculate for the coefficient b in the linear regression equation describing the sample data below.A sample of 40 individuals collects their shoe size and the height (cm) for CSI data. The scatter plot and results from a simple linear regression are recorded: HEIGHT = 126.76238 + 4.8782178 SHOE SIZE Sample size: 40R (correlation coefficient) = 0.77918855P-value < 0.0001 (a) Does the scatterplot and results show a linear correlation between shoe size and height? (b) How can you tell? (c) Will it be appropriate to use the linear regression equation given in the output? (d) Krusty the Clown wears size 8.5 shoes. According to the linear regression equation, how tall is Krusty the Clown? (e) Sideshow Bob wears size 14 shoes. According to the linear regression equation, how tall is Sideshow Bob?
