18. 17. The number of murders and robberies per 100,000 population for a random selection of states areshown. Given the equation of the regression line is y' = 25.333x- 13.151, predict the number ofrobberies when x = 4.5 murders.Murders, xRobberies, y2.42.75.62.62.13.36.65.725.314.3151.691.1804917.395.818. A random sample of non-industrialized countries was selected, and the life expectancy in years islisted for both men and women. Given that the correlation coefficient is significant, find theequation of the regression line.Men, x59.772.941.946.250.343.2Women, y63.877.844.548.354.043.519

Men,x 59.7 72.9 41.9 46.2 50.3 43.2 Men,y 63.8 77.8 44.5 48.3 54 43.5

A random sample of non-industrialized countries was selected, and the life expectancy in years is listed for both men and women. Given that the correlation coefficient is significant, find the equation of the regression line. Men, x 59.7 72.9 41.9 46.2 50.3 43.2 Women, y 63.8 77.8 44.5 48.3 54.0 43.5

A random sample of non-industrialized countries was selected, and the life expectancy in years is listed for both men and women. Given that the correlation coefficient is significant, find the equation of the regression line. Men, x 59.7 72.9 41.9 46.2 50.3 43.2 Women, y 63.8 77.8 44.5 48.3 54.0 43.5

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000
Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of people, the linear correlation coefficient is 0.930 and the equation of the regression line is y=−10.69+1.11x, where x represents the IQ score of the twin born first. Also, the 20 x values have a mean of 98.28 and the 20 y values have a mean of 98.5. What is the best predicted IQ of the twin born second, given that the twin born first has an IQ of 92? Use a significance level of 0.05.LOADING... Click the icon to view the critical values of the Pearson correlation coefficient r.Question content area bottomPart 1The best predicted IQ of the twin born second is enter your response here.(Round to two decimal places as needed.)
9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5
17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…
If other factors are held constant and the Pearson correlation value between X and Y is r = 0.80, then the regression equation will tend to produce more accurate predictions than would be obtained if the Pearson correlation value was r = 0.60. True or False
Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.04, standard error for the coefficient of z is 0.01, and the sample size is 20. Can we conclude that advertising expenditure is a statistically significant variable?
Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of people, the linear correlation coefficient is r = 0.914 and the equation of the regression line is y = 9.87+0.9x, where x represents the IQ score of the twin born first and y represents the IQ score of the twin born second. What is the bestpredicted IQ of the twin born second, given that the twin born first has an IQ of 107?What does the r value tell you about the relationship between the IQ scores of twins?What is the Value for r squared? What does the r squared statiscic mean in this scenario?
Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of people, the linear correlation coefficient is 0.892 and the equation of the regression line is Modifying Above y= -1.91 + 1.01 x, where x represents the IQ score of the twin born the second. Also, the 20 x values have a mean of 100.07 and the 20 y values have a mean of 98.8 What is the best predicted IQ of the twin born first twin born first,given that the twin born second twin born secondhas an IQ of 96?Use a significance level of 0.05. Click the icon to view the critical values of the Pearson correlation coefficient r. Critical Values of the Pearson Correlation Coefficient r NOTE: To test H0: rhoρequals=0 against H1: rhoρnot equals≠0, reject H0 if the absolute value of r is greater than the critical value in the table. n a=0.05 a=0.01 4 0.950 0.990 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10…
If x and y in a regression model are totally unrelated, _______. the coefficient of determination would be 0 the MSE would be 0s the SSE would be 0 the correlation coefficient would be -1 the coefficient of determination would be 1
η =8, sum x=28, sum y=384, Sigma xy=480, Sigma x^ 2 =134 Find the estimated regression line
For a set of data: x = (0,1,2,3,4,5,6) and y=(36, 28, 25, 24, 23, 21, 19), is it wise to use a linear regression to extrapolate data for x = 50? Solution: Since the coefficient of determination is 0.8582, the linear model is a reasonably good fit for the data, so extrapolation for any x-value is acceptable. What is wrong with this solution?