%3D 7. The correlation coefficient between the variables X and Y isr 0.60. If o,= 1.50, o, = 2.00, X = 10, Y = 20. Find the equation of the regression lines, (i) Y on X (ii) X on Y.
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.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?
- A set of n = 4 pairs of X and Y values has a Pearson correlation of r = 0.60 and SSY = 200. The standard error of estimate for the regression equation is _______. a. 8 points b. 10 points c. 6 points d. 4 pointsWhich of the following statements is NOT true? a.If the correlation coefficent, rr, is negative, then the slope of the regression line must always be negative. b.For variables x and y, the value of the correlation coefficent will not change c.if the units of x and y are changed, (i.e., if both x and y are changed from say inches to meters) d.If r≠0r≠0 , then a significant linear correlation will exist between the two variables e.The value of the correlation coefficient must be within the interval: −1≤r≤1The equation of the regression line between two variables x (independent variable) and y (dependent variable) is given by y^=−3x+2; and the correlation coefficient is r=−.95. The possible x-values range from 1 to 10. Based on the given r, which of the following conclusions may be made? x and y are moderately correlated, and y tends to increase as x is increased. x and y are strongly correlated, and y tends to increase as x is increased. x and y are very weakly correlated. x and y are strongly correlated, and y tends to increase as x is decreased. There is no way to tell the relationship between x and y.
- Suppose that you run a correlation and find the correlation coefficient is 0.421 and the regression equation is ˆy=2.2x+6.96y^=2.2x+6.96. The center of your x-data was 5.2 and the center of your y-data was 18.6.If the critical value is .396, use the appropriate method to predict the yy value when xx is 6.8There is a relation between the following variables as y = 1 / (a * x ^ b) (x ^ b means x over b) a) Calculate the correlation coefficient and interpret the degree of the relationship? b) Estimate the y-value for x = 4.3 and the x-value for y = 0.90 by obtaining the regression equationThe equation of the regression line between two variables xx (independent variable) and yy (dependent variable) is given by y^=−3x+2y^=−3x+2; and the correlation coefficient is r=−.95.r=−.95. The possible xx-values range from 1 to 10. Predict yy if x=3.5x=3.5.