Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y = X y 26.95 5 6 27.76 7 29.07 8 9 29.28 32.39 10 30.1 11 34.71 X +
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Olympic 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?Annual high temperatures in a certain location have been tracked for several years. Let XX represent the year and YY the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).y = x + x y 2 4.13 3 1.72 4 4.21 5 1.9 6 4.69 7 1.68 8 2.27 9 1.86 10 2.25 11 3.14 12 1.53 13 0.72 14 0.51 15 3.5
- Annual high temperatures in a certain location have been tracked for several years. Let Xrepresent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).y = x + x y 4 14.9 5 17 6 18.7 7 23.2 8 23.2 9 28 10 30.8 11 34.4 12 36.3 13 37.5 14 42.6 15 42.9 16 47.4Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).y = x + x y 5 8.3 6 9.06 7 9.12 8 11.98 9 8.44 10 12.4 11 9.56 12 11.22 13 10.08 14 10.74A 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 points
- The prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Calories, x Sodium, y150 410180 460120 320120 36070 290190 540 (a) x=160 calories (b) x=90 calories (c) x=130 calories (d) x=220 calories Y=_____x+(___)Use the given data to find the scatterplot, equation of the regression line, and prediction. x 1.2 1.4 1.6 1.8 2.0 y 54 53 55 54 56 Let α=0.05 Scatterplot from the calculator: What is the linear regression equation? (Round to 3 decimal places) ^ y= _________________________________________________________________ r = _______________ critical value from table: ________________ Is there a strong enough linear correlation to use the regression equation given? ___________ Explain why? _____________________________________________________ What is the best predicted y-value when x=1.9 ? _______________
- For these (x,y) pairs of data points: 1,5 3,7 4,6 5,8 7,9 Compute b1. Compute b0. What is the equation of the regression line?A researcher wants to know if there is a significant correlation between hours spent studying for an exam (X) and exam performance (Y). Level of significance is 0.05, degrees of freedom is 3, and the critical value is 0.878. Interpret the strength and direction of the correlation, calculate and interpret the coefficient of determination, then develop the simple regression equation for the two variables. X (Time Spent Studying in Hours) Y (Exam Performance, 0 to 100) 3 56 6 77 7 79 8 70 11 96 Mean 7.00 75.60 SD 2.92 14.54 For this question, on your hand calculation document clearly state: a) the null hypothesis, b) the alternative hypothesis, c) the alpha level you are using, d) the critical value, e) process for calculating r, f) your decision about the null hypothesis, g) the coefficient of determination, h) and regression equation. This is what I will be marking. You may also enter your responses here, but it is…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.
