You run a regression analysis on a bivariate set of data (n=32n=32). With ¯x=46.5x¯=46.5 and ¯y=37.1y¯=37.1, you obtain the regression equationy=−1.725x+12.184y=-1.725x+12.184with a correlation coefficient of r=−0.75r=-0.75. You want to predict what value (on average) for the response variable will be obtained from a value of 150 as the explanatory variable. What is the predicted response value? y =

You run a regression analysis on a bivariate set of data (n=32n=32). With ¯x=46.5x¯=46.5 and ¯y=37.1y¯=37.1, you obtain the regression equationy=−1.725x+12.184y=-1.725x+12.184with a correlation coefficient of r=−0.75r=-0.75. You want to predict what value (on average) for the response variable will be obtained from a value of 150 as the explanatory variable. What is the predicted response value? y =

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?
If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot displays a linear trend, can you use the regression equation to make predictions, assuming your x-values are within the domain of the data set? Choose your answer from the multiple choice answers below A.) Yes, because rcrit = 0.396 and the regression coefficient, r, is less than this value. B.) Yes, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. C.) No, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. D.) No, because rcrit = 0.396 and the regression coefficient, r, is less than this value.
A sample of n = 15 pairs of X and Y scores produces a Pearson correlation of r = 0.45, SSY = 90. a) If the regression equation was found for these scores, how much of the Y variability would be predicted by the regression equation (SSregression) and how much would not be predicted (SSresidual)? b) Does the regression equation predict a significant portion of the variability for the Y scores? (Equivalently, is the Pearson correlation significant?)
In a study of possible correlation between the height in cm (X) and the weight in kg (Y) of chimpanzees, a sample of 40 animals produces a correlation coefficient of r=0.813 and a regression line with equation Y=0.34X+19.5. What is the expected weight of a chimpanzee that is 157 cm tall? Round off final answer to 2 decimal places.
If other factors are held constant, if the Pearson correlation between X and Y is r = 0.50, then the regression equation will produce more accurate predictions than would be obtained if r = 0.70. True or false?
A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.
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. Group of answer choices True False
In a linear regression model, calculate the slope of the line, b1, when the correlation coefficient is r = -0.37, and the standard deviations of the predictor variable equals sx = 0.552 and the standard deviation of the response variable equals sy = 0.552. Only round your final answer to 2 decimal places.
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?
The average midterm score in a large statistics class was 70 with an SD of 10. The average final score in the same class was 65 with an SD of 15. The correlation coefficient between midterm and final scores was r=0.6. Using the regression line, we predict the final score of a student with a midterm score of 60 to be , but this prediction is likely to be off by about . Fill in the blanks, rounding each answer to one decimal point.
The average midterm score in a large statistics class was 65 with an SD of 15. The average final score in the same class was 70 with an SD of 10. The correlation coefficient between midterm and final scores was r-0.6. Using the regression line, we predict the final score of a student with a midterm score of 80 to be but this prediction is likely to be off by about
If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that y and x are positively correlated. True or false?