Statistics A statistical program is recommended.and X2.Consider the following data for a dependent variable y and two independent variables, X1X1 X2 y30 12 94472551517440 5365910 1087617 11216 17819 175947 17012 11713 14216 211The estimated regression equation for the data isŷ = -18.4 +2.01x₁ + 4.74x₂.x2(a) Develop a 95% confidence interval for the mean value of y when X1 = 36 and x₂ = 12. (Round your answers to three decimal places.)to(b) Develop a 95% prediction interval for y when X1to= 36 and X2= 12. (Round your answers to three decimal places.)

I used R-software for calculations.1> x1=c(30,47,25,51,40,51,74,36,59,76) 2>…

A statistical program is recommended. Consider the following data for a dependent variable y and two independent variables, X₁ and X2. X₁ X₂ y 30 47 10 108 25 12 94 51 16 17 112 40 5 94 36 51 19 175 74 7 170 76 178 12 117 59 13 142 16 211 The estimated regression equation for the data is y = -18.4 +2.01x₁ + 4.74x2. (a) Develop a 95% confidence interval for the mean value of y when x₁ = 36 and x₂ = 12. (Round your answers to three decimal places.) to (b) Develop a 95% prediction interval for y when X₁ = 36 and x₂ = 12. (Round your answers to three decimal places.) to

A statistical program is recommended. Consider the following data for a dependent variable y and two independent variables, X₁ and X2. X₁ X₂ y 30 47 10 108 25 12 94 51 16 17 112 40 5 94 36 51 19 175 74 7 170 76 178 12 117 59 13 142 16 211 The estimated regression equation for the data is y = -18.4 +2.01x₁ + 4.74x2. (a) Develop a 95% confidence interval for the mean value of y when x₁ = 36 and x₂ = 12. (Round your answers to three decimal places.) to (b) Develop a 95% prediction interval for y when X₁ = 36 and x₂ = 12. (Round your answers to three decimal places.) to

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=...

See similar textbooks

Similar questions

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?
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
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
Consider the data. xi 1 2 3 4 5 yi 4 8 4 12 12 The estimated regression equation for these data is ŷ = 2.00 + 2.00x. (a) Compute SSE, SST, and SSR using equations SSE = Σ(yi − ŷi)2, SST = Σ(yi − y)2, and SSR = Σ(ŷi − y)2. SSE=? SST=? SSR=? (b) Compute the coefficient of determination r2. r2 = ?? Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) -The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line. -The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line. -The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. -The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.…
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
Shown in the SPSS output for creating a regression equation to predict students' attitudes toward statistics from their attitudes toward Ariana grande and beer. Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 4.974 0.590 8.432 0.000 AttAriana 0.264 0.155 0.256 1.701 0.097 Attbeer - 0.309 0.122 - 0.381 - 2.536 0.015 Coefficients a a Dependent Variable: Attstatistics Which of these represents the correct regression equation for this information? a. Y = 0.59 +…
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.)
The following estimated regression equation is based on 10 observations yhat = 30.12 + .60x1 + .48x2 SST = 680.3, SSR= 601.4, Sb1 = .0813 and Sb2 = .0567 a. Compute MSR and MSE b. Compute F and perform the appropriate F test. Use alpha = .05. c. Perform a t test for the significance of B1. Use alpha = .05. d. Perform a t test for the significance of B2. Use alpha = .05.
For observed data y=(y1,…,yn)y=(y1,…,yn) with n=21n=21, the above linear regression model was fitted in R, with the following output: >n = 21 >xi = seq(0, n-1,1)/(n-1) >p1 =2*xi-1 >p2 =6*xi^2- 6*xi+1-1/(n-1) > summary(lm(y ~ p1+p2)) Call: lm(formula = y ~ p1 + p2) Residuals: Min 1Q Median 3Q Max -0.5258 -0.2153 0.0813 0.1770 0.4669 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.004238 0.063450 -0.067 0.947 p1 1.181260 0.104784 11.273 1.37e-09 *** p2 -0.953388 0.129422 -7.366 7.77e-07 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.2908 on 18 degrees of freedom Multiple R-squared: 0.9097, Adjusted R-squared: 0.8997 F-statistic: 90.68 on 2 and 18 DF, p-value: 3.989e-10 Write this linear regression model in the vector form and answer the following questions, using the above R output where necessary.
Given are data for two variables, x and y. xi 6 11 15 18 20 yi 5 9 13 19 30 An estimated regression equation for these data is yhat=-7.24+1.6x a) Compute the residuals. (Round your answers to two decimal places.) b) Compute the standardized residuals. (Round your answers to two decimal places.) Ans both..otherwise don't answer
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 4 11 14 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.