What is the equation for the regression line if n = 7, Ex= 69, Ey= 528, ry = 4754and x² = 825? ý = -3.11 + 106.09x ý = 109.64 – 2.17x ý = 106.09 - 3.11a. O ŷ =-2.17 + 109.64x
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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?There is a linear regression: Yi = B0+ B1(Xi^2)+ ei present, where Xi is squared. ei ∼ N(0,σ2). How would I derive LSE for B0 and B1 and their variance?It is known that the linear regression equation: y= -2.88+1.77x, with a coefficient of determination of 0.81. Based on the two information, the correlation coefficient is
- Assume a person got score of 32.5 on Test A and a score of 95.25 on Test B. Using the regression equation (B' = 2.3A + 9.5), what is the error of prediction for this person?what is teh regression equation for (2,44), (5,66), (4,57), (8,86) ,(5,67) where x is snowfall and y is yieldIQ scores were obtained from randomly selected adopted children living together. For 20 such pairs of children, the linear correlation coefficient is 0.027 and the equation of the regression line is y=-3.22+1.02x, where x represents the IQ score of the older child. Also, the 20 x values have a mean of 104.2 and the 20 y values have a mean of 103.1. What is the best predicted IQ of a younger adopted child, given that the older adopted child in the same family has an IQ of 110
- For the 2011 season, suppose the average number of passing yards per attempt for a certain NFL team was 6.1. Use the estimated regression equation developed in part (c) to predict the percentage of games won by that NFL team. (Note: For the 2011 season, suppose this NFL team's record was 7 wins and 9 losses. Round your answer to the nearest integer.)You spilled water on your calculations from (a) and can't remember what your estimated regression parameters are. But you do have two possible estimated errors for each of your initial four observations:For 40 eruptions of the Old Faithful geyser in Yellowstone National Park, duration times (sec) were recorded along with the heights (ft) of the eruptions. The linear correlation coefficient is r = 0.0915 and the regression equation is = 119 + 0.0331x, where x represents duration time. The mean of the 40 duration times is 245.0 sec and the mean of the 40 heights is 127.2 ft. What is the best predicted height of an eruption with a duration time of 120 min?
- I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?The table below shows the numbers of new-vehicle sales for company 1 and company 2 for 11 years. Construct and interpret a 90% prediction interval for new vehicle sales for company 2 when the number of new vehicles sold by company 1 is 2687 thousand. The equation of the regression line is y = 1.207x + 398.378 "We can be 90% confident that when the new-vehicle sales for company 1 is 2687 thousand, the new-vehicle sales for company 2 will be between ___ and ___ thousand."If the equation for the regression line is y^ prime =8x+7 then a value of x = - 2 will result a predicted value for y