Based on the data shown below, calculate the correlation coefficient (to three decimal places). This is the 'r' value you get when you do the regression. y 1 31.4 2 29.4 28 4 27.9 5 24.4 6 22.4 7 21.9 8 20.8 9 19.5 10 15.3 11 15.4 12 11.4 X W|N 3 45 78
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- 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.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 data shown below, calculate the correlation coefficient (to three decimal places). This is the 'r' value you get when you do the regression. x y 4 22.6 5 23.9 6 22.5 7 22 8 23.3 9 23 10 22.8 11 20.2 12 21
- Based on the data shown below, calculate the correlation coefficient (to three decimal places). This is the 'r' value you get when you do the regression. x456789101112131415161718 y29.228.0529.928.1525.124.0524.924.7522.823.6522.219.2518.618.1520.6(c) Find the linear correlation coefficient for these data. (Round your answer to four decimal places.) r= ?Compute for the necessary correlational analysis based on the given data. The following data, adapted from Montgomery, Peck, and Vining (2001), present the number of certified mental defectives per 10,000 of estimated population in the United Kingdom ( y) and the number of radio receiver licenses issued (x) by the BBC (in millions) for the years 1924 through 1937. Fit a regression model relating y and x. Comment on the model. Specifically, does the existence of a strong correlation imply a cause-and-effect relationship?
- A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n=15 college students. The SAT scores have a mean of M=580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation, r, then find r2.) C) Does the regression equation account for a significant portion of the variance in GPA? Use alpha = 0.05 to evaluate the F-ratio. A) b=0.00375; a=0.925; Y (hat) = 0.00375X+0.925 B) r= 0.5 r^2= 0.25A professor obtains SAT scores and freshman grade point averages (GPA) for a group of n=15 college students. The SAT scores have a mean of M=580 with SS=22,400, and GPA has a mean of 3.10 with SS=1.26, and SP=84. a. Find the regression equation for predicting GPA from SAT scores. b. What percentage of the variance in GPA is accounted for by the regression equation? (Compute the correlation, r, then find r2.) c. Does the regression equation account for a significant portion of the variance in GPA? Use α=.05 to evaluate the F-ratio.Find the Pearson r Correlation Coefficient: r = Blank 1 Find the equation of the regression line: y = Blank 2x + Blank 3 Estimate the amount of particulate removed when the daily rainfall is x = 4.8 units: Blank 4 μg/m3
- Which of the following best describes a regression coefficient in a bivariate setting? a. The change in Y predicted by a unit change in X b. The slope of a line that minimizes the sum of squared residuals c. The correlation coefficient multiplied by SDy/SDx d. All of the aboveThe scale of the correlation coefficient is: a. nominal b. ordinal c. ratioA professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation r, then find r^2.) Does the regression equation account for a significant portion of the variance in GPA? Use α = .05 to evaluate the F-ratio.