2. Consider the following data for two variables, x and y. 32 18 15 26 у 10 20 21 16 22 a. Develop an estimated regression equation for the data of the form ŷ = b, + b,x. Comment on the adequacy of this equation for predicting y.
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- The 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?Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 6 6 11 13 Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 2.
- 1. Consider the following data for two variables, x and y.x 22 24 26 30 35 40y 12 21 33 35 40 36a. Develop an estimated regression equation for the data of the form yˆ = b0 + b1x.b. Use the results from part (a) to test for a significant relationship between x and y.Use a = .05.c. Develop a scatter diagram for the data. Does the scatter diagram suggest an estimatedregression equation of the form yˆ = b0 + b1x + b2x2? Explain.d. Develop an estimated regression equation for the data of the form yˆ = b0 + b1x +b2x2.e. Refer to part (d). Is the relationship between x, x2, and y significant? Use a = .05.f. Predict the value of y when x = 25.Given are five observations for two variables, x and y. xi 3 12 6 20 14 yi 55 45 50 15 20 #1) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. y= #2) Use the estimated regression equation to predict the value of y when x = 13.Consider the following data for two variables, x and y. x 9 32 18 15 26 y 9 19 20 15 22 Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to two decimal places and b1 to three decimal places and b2 to four decimal places.) ŷ = (c) Use the model from part (b) to predict the value of y when x = 20. (Round your answer to two decimal places.)
- Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 6 5 9 14 Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal). y^= + x Use the estimated regression equation to predict the value of y when x = 5 (to 1 decimal).y^ =The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown below. Find the regression equation. y = 34.661 + 0.433x y = 0.777 + 12.0623x y = 12.0623 + 0.777x y = 34.661 - 0.433xThe director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergent (R). The marketing director collects 36 weekly observations on S, A and R to estimate the following multiple regression equation: S = a + bA + cR .where, S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10% level or better.DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON FOBSERVATIONS: 36 0.2247 4.781 0.0150VARIABLE PARAMETER STANDARD T-RATIO P-VALUE ESTIMATE ERRORINTERCEPT 175086.0 63821.0 2.74 0.0098A 0.8550 0.3250…
- A statistical program is recommended. Consider the following data for two variables, x and y. x 22 24 26 30 35 40 y 12 22 34 36 41 37 (d) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to one decimal place and b1 to two decimal places and b2 to four decimal places.) ŷ = −175+12.63x−.1837x2 Use the results from part (d) to test for a significant relationship between x, x2, and y. Use α = 0.05. Is the relationship between x, x2, and y significant? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.)Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 18 9 26 23 Develop the estimated regression equation for these data. ŷ = (c) Use the estimated regression equation to predict the value of y when x = 20.Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 9 18 8 25 21 (b) Develop the estimated regression equation for these data. ŷ = (c) Use the estimated regression equation to predict the value of y when x = 13.
