X bx. y 12.4 0.3 18.3 9.7 -0.6 3.9 -8.9 -2.7 17.1 -4.5 ariable Suppose that a simple linear regression model is used to estimate the relationship between X and Y, using y = a
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How to determine a and b from table?
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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?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.)
- Consider the following data for two variables, x and y. x 22 24 26 30 35 40 y 11 21 34 36 39 36 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 = (e) Use the results from part (d) to test for a significant relationship between x, x2, and y. Use ? = 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.) p-value = (f) Use the model from part (d) to predict the value of y when x = 25. (Round your answer to three decimal places.)Consider the following data set. x 1 2 3 4 5 y 2.2 2 1.9 1.6 1.1 Find the equation of the regression line. (Round the values to two decimal places.) y =Use the sample linear regression line Y^=2+3X for the data points below to answer the following questions. X 0 3 7 10 Y 5 5 27 31 1) What is the fitted value when X2=3? 2) What is the regression residual when X2=3?
- Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 94 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 211 (a) Develop an estimated regression equation relating y to x1. (Round your numerical values to one decimal place.) ŷ = Predict y if x1 = 51. (Round your answer to one decimal place.) (b) Develop an estimated regression equation relating y to x2. (Round your numerical values to one decimal place.) ŷ = Predict y if x2 = 19. (Round your answer to one decimal place.) (c) Develop an estimated regression equation relating y to x1 and x2. (Round your numerical values to one decimal place.) ŷ = Predict y if x1 = 51 and x2 = 19. (Round your answer to one decimal place.)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.)Consider the following data: A. Find the equation of the regression line. B. Estimate the value of y when x = 15 x 1 2 3 4 5 6 7 y 2 6 4 8 12 10 12
- The following scores represent a nurse’s assessment (X) and a physician’s assessment (Y) of the condition of 10 patients at time of admission to a trauma centre: X: 18 13 18 15 10 12 8 4 7 3 Y: 23 20 18 16 14 11 10 7 6 4 a) Obtain the regression equation. b) What is the predicted physician’s assessment for a nurse’s assessment of; 16 scores? 21 scores? c) Distinguish between extrapolation and interpolationFor the following set of scores: X Y 0 16 1 6 2 9 3 0 4 9 (a) Compute the Pearson correlation.r = (b) Find the regression equation for predicting Y from X.Y = X +A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = -20; SSx = 4; My = 7; Mx = 3 What is b equal to? What is a equal to? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?
