You have the results of a simple linear regression based on state-level data and the District of Columbia, a total of N = (a) The estimated error variance 2 = 2.00. What is the sum of the squared least squares residuals? (b) The estimated variance of b₂ is 0.25, what is the standard error of b₂? What is the value of ✗(xi — ñ)²? - = 52 observations. (c) Suppose the dependent variable y; is the state's mean income (in thousands of dollars) of males who are 18 years of age or older and percentage of males 18 years or older who are high school graduates. Interpret the slope estimate 62 = 0.10. (d) Suppose = 50.00 and y = 10.00, what is the estimate of the intercept parameter? (e) Given the results in (b) and (d), what is Σx?? Ꮖ ; the (f) For the state of Arkansas the value of yi parts (c) and (d)). = 12 and the value of xi = 60. Compute the least squares residual for Arkansas. (Hint: Use the information in

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?

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?

Two lines of regression are given by 5x+7y-22=0 and 6x+2y-22=0. If the variance of y is 15, find the standard deviation of x.