If Linear correlation coefficient r = 0.794556 Coefficient of determination = 0.631319 Equation of regression line is y = 16.5523 + 0.725938x then both variables are moving in the same direction. A) True False B
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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.In a simple linear regression model with one predictor variable, what is the coefficient of determination (R-squared) if the Pearson's correlation coefficient between the predictor and response variable is 0.6?
- on the basis of the value of linear correlation coefficient, would you conclude, at the /r/>0.9 level, that the data can be reasonably modeled linear equation?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?)If there is no significant correlation between the response and explanatory variables, would the slope of the regression line be (a) positive (b) negative (c) zero?
- 24) If the R-square value for a simple linear regression model is 0.80 and the regression line has anegative slope, the correlation coefficient describing the relationship between the two variables is_____________.If the correlation coefficient is zero, the slope of a linear regression line will be a. positive b. negative c. positive or negativeIf 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
- 1) Indicate whether the following statements are true or false. Explain why and show your work. c) In the regression Y= B1+ B2X + B3Z+u , if there is a strong linear correlation between X and Z, then it is more likely you fail to reject the null hypotheses that individual slope parameters are insignificant.In simple linear regression, most often we perform a two-tail test of the population slope 1 to determine whether there is sufficient evidence to infer that a linear relationship exists. The null hypothesis is stated as:What are the assumptions of simple linear regression (and as a consequence the pearson’s r correlation)?