Consider the following data for a dependent variable y and two independent variables, x, and x2.X1 x2y301295471010825171125116178405945119175747170361211759131427616212The estimated regression equation for these data isý = -18.52 + 2.01x, + 4.75x2.14,109.8, 5b,= 0.2464, andHere, SST = 15,234.1, SSR == 0.9457.(a) Test for a significant relationship among x,, x,, and y. Use a = 0.05.State the null and alternative hypotheses.O Ho: B1 = 82 = 0H: One or more of the parameters is not equal to zero.O Ho: B, < B2H: B, 2 82O Ho: B, +0 and B2 = 0H: B, = 0 and B2 + 0O Ho: B1 > B2H: B, s B2O Ho: B, + 0 and 82 # 0H: One or more of the parameters is equal to zero.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 = Find the p-value. (Round your answer to three decimal places.)p-value =State your conclusion.O Do not reject H,. There is sufficient evidence to conclude that there is a significant relationship among the variables.O Reject H,. There is sufficient evidence to conclude that there is a significant relationship among the variables.O Reject H,. Theres insufficient evidence to conclude that there is a significant relationship among the variables.O Do not reject H,. There is insufficient evidence to conclude that there is a significant relationship among the variables.(b) Is 8, significant? Use a = 0.05.State the null and alternative hypotheses.O Ho: B, = 0H: B, > 0O Ho: B1 > 0O H;: B, +0H: B = 0O H;: B, = 0H: B + 0O Họ: B1 < 0H,: B, 20Find 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 =State your conclusion.O Do not reject H,. There is insufficient evidence to conclude that 8, is significant.Reject H.. There is insufficient evidence to conclude that 8, is significant.O Reject H. There is sufficient evidence to conclude that 8, is significant.O Do not reject H,. There is sufficient evidence to conclude that 8, is significant.

Consider the following data for a dependent variable y and two independent variables, x, and x,. X1 X2 Y 30 12 95 47 10 108 25 17 112 51 16 178 40 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 212 The estimated regression equation for these data is ý --18.52 + 2.01x, + 4.75x2. Here, SST - 15,234.1, SSR - 14,109.8, s,, - 0.2464, and s. - 0.9457. (a) Test for a significant relationship among x,, X2, and y. Use a = 0.05. State the null and alternative hypotheses. O Ho: B - P2 - 0 H,: One or more of the parameters is not equal to zero. O Ho: B1 « B2 O Ho: B, * 0 and B2 - 0 H,: B, - 0 and B, + 0 O Ho: B1 > B2 O Ho: B *0 and B2 0 H,: One or more of the parameters is equal to zero. 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.) Oavalue

Consider the following data for a dependent variable y and two independent variables, x, and x,. X1 X2 Y 30 12 95 47 10 108 25 17 112 51 16 178 40 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 212 The estimated regression equation for these data is ý --18.52 + 2.01x, + 4.75x2. Here, SST - 15,234.1, SSR - 14,109.8, s,, - 0.2464, and s. - 0.9457. (a) Test for a significant relationship among x,, X2, and y. Use a = 0.05. State the null and alternative hypotheses. O Ho: B - P2 - 0 H,: One or more of the parameters is not equal to zero. O Ho: B1 « B2 O Ho: B, * 0 and B2 - 0 H,: B, - 0 and B, + 0 O Ho: B1 > B2 O Ho: B *0 and B2 0 H,: One or more of the parameters is equal to zero. 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.) Oavalue

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...

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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 sample regressions for the linear and quadratic models along with their respective R2 and adjusted R2. Linear Quadratic Intercept 13.3087 1.7656 x 0.3392 4.0966 x2 NA -0.2528 R2 0.1317 0.5844 Adjusted R2 0.0232 0.4657 Choose the model with the best fit, and then predict y for x = 4, 8, and 12. ROUND TO TWO DECIMAL PLACES. x Predicted y 4 8 12
The following sample of observations was randomly selected. x 5 3 6 3 4 4 6 8 y 13 15 7 12 13 11 9 5 a. Determine the regression equation.b. Determine the value of ŷ when x is 7
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 = −18.4+2+4.74x2 Predict y if x1 = 76. (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 = 16. (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 = 76 and x2 = 16. (Round your answer to one decimal place.)
41. Which of the following is the multiple regression model for the data? (a) y = -0.11050 + 2.10797x1 + 0.40717x2 (b) y = -0.11050 + 0.40717x1 + 2.10797x2 (c) y = 0.23563 + 0.00062x1 + 0.23626x2 (d) none (e) y = -0.44187 + 2.42120x1 + 0.36135x2
For the following values of SSX, SSY, and SP, the Pearson correlation coefficient (r) is ______ and the slope of the regression line (b) is _______. SSX SSY SP 100 200 90
The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: Give the following: a. linear regression line and equation b. computation of the coefficient of determination ?^2 c. Computation of the coefficient of correlation ? d. Estimate the final examination grade of a student who received a grade of 85 on the midterm report.
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.)
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 - 0.433x
Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 95 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 The estimated regression equation for these data is ŷ = −17.85 + 2.00x1 + 4.73x2. Here, SST = 15,091.6, SSR = 13,969.7, sb1 = 0.2462, and sb2 = 0.9447. (a) Test for a significant relationship among x1, x2, and y. Use ? = 0.05. State the null and alternative hypotheses. H0: ?1 ≠ 0 and ?2 ≠ 0Ha: One or more of the parameters is equal to zero.H0: ?1 < ?2Ha: ?1 ≥ ?2 H0: ?1 = ?2 = 0Ha: One or more of the parameters is not equal to zero.H0: ?1 ≠ 0 and ?2 = 0Ha: ?1 = 0 and ?2 ≠ 0H0: ?1 > ?2Ha: ?1 ≤ ?2 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 = State your conclusion. Do not reject H0. There is insufficient evidence to conclude…
Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 95 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 The estimated regression equation for these data is ŷ = −17.85 + 2.00x1 + 4.73x2. Here, SST = 15,091.6, SSR = 13,969.7, sb1 = 0.2462, and sb2 = 0.9447. #1) Find the value of the test statistic. (Round your answer to two decimal places.) #2)Find the p-value. (Round your answer to three decimal places.) p-value =