Consider the following data for a dependent variable y and two independent variables, ¤1 and ¤2. 30 12 94 47 11 109 25 17 113 50 17 178 40 6 95 52 20 175 75 8 171 37 12 118 60 13 143 76 16 211 The estimated regression equation for these data is ŷ = -20.03 + 1.95x1 + 4.92x2 Here SST = 14,990.1, SSR = 13,918.4, 8, = 0.2382, and si, = 0.9506. a. Test for a significant relationship among #1, x2, and y. Use a = 0.05. F = 45.46 (to 2 decimals) The p-value is less than 0.01 At a = 0.05, the overall model is significant b. Is B1 significant? Use a = 0.05 (to 2 decimals). Use t table. te, = The p-value is less than 0.01

Consider the following data for a dependent variable y and two independent variables, ¤1 and ¤2. 30 12 94 47 11 109 25 17 113 50 17 178 40 6 95 52 20 175 75 8 171 37 12 118 60 13 143 76 16 211 The estimated regression equation for these data is ŷ = -20.03 + 1.95x1 + 4.92x2 Here SST = 14,990.1, SSR = 13,918.4, 8, = 0.2382, and si, = 0.9506. a. Test for a significant relationship among #1, x2, and y. Use a = 0.05. F = 45.46 (to 2 decimals) The p-value is less than 0.01 At a = 0.05, the overall model is significant b. Is B1 significant? Use a = 0.05 (to 2 decimals). Use t table. te, = The p-value is less than 0.01

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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Ten observations were provided for a dependent variable y and two independent variables x1 and x2; for these data, SST = 15,189.8 and SSR = 14,056.9. (a) Compute R2. (Round your answer to three decimal places.) R2 = (b) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (c) Does the estimated regression equation explain a large amount of the variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to one decimal place.) , after adjusting for the number of independent variables in the model, we see that % of the variability in y has been accounted for.
4.For a sample of 12 observations, a businessman wants to regress the price (in dollar) of the laptop (Y) on the processor's speed (X). The summary results of the observations are given below. Σx = 19.8 , Σy = 24798, Σxy = 431882 Σx^2 = 33.88, Σγ^2 = 57365692 (b)Find the fitted regression line of the price of laptop on processor speed. (c) Find the predicted price of the laptop (y) for the processor speed x-1.9. (d) Compute the coefficient of determination and comment.
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If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot displays a linear trend, can you use the regression equation to make predictions, assuming your x-values are within the domain of the data set? Choose your answer from the multiple choice answers below A.) Yes, because rcrit = 0.396 and the regression coefficient, r, is less than this value. B.) Yes, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. C.) No, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. D.) No, because rcrit = 0.396 and the regression coefficient, r, is less than this value.
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.)
The following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ŷ = 28 + 15x1 + 9x2 The data used to develop the model came from a survey of 10 stores; for those data, SST = 18,000 and SSR = 13,140. 1. Compute R2 2. Compute Ra2 3. The adjusted coefficient of determination shows that ____ % of the variability has been explained by the two independent variables.
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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
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…