Given the data in the table below for the dependent variable Y and independent variables X1, X2, and X3 that is to be used in the estimation of the linear regression model E(Y)=DB0 +B1X1+B2X2+B3X3: Y X1 X2 X3 10 3. 4 8. 12 4 6. 14 3 6. 15 3 11 4 28 1 0. 7. 2 24 3. 25 3 6. 20 3 4 Copy this data and paste it in the excel sheet and make the following computations and then copy the solutions back into the text boxes: a) (X'X), that is "X-transpose-X " matrix b) inverse of (X'X) c) X'Y, that is "X-transpose-Y" d) Beta -vector, that is the vector of the estimates of the parameters BO, B1, B2, and B3.

Given the data in the table below for the dependent variable Y and independent variables X1, X2, and X3 that is to be used in the estimation of the linear regression model E(Y)=DB0 +B1X1+B2X2+B3X3: Y X1 X2 X3 10 3. 4 8. 12 4 6. 14 3 6. 15 3 11 4 28 1 0. 7. 2 24 3. 25 3 6. 20 3 4 Copy this data and paste it in the excel sheet and make the following computations and then copy the solutions back into the text boxes: a) (X'X), that is "X-transpose-X " matrix b) inverse of (X'X) c) X'Y, that is "X-transpose-Y" d) Beta -vector, that is the vector of the estimates of the parameters BO, B1, B2, and B3.

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?
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 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 9 32 18 15 26 y 9 20 22 17 23 A. Develop an estimated regression equation for the data of the form ŷ = b0 + b1x. (Round b0 to two decimal places and b1 to three decimal places.) B. 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.) C. Use the model from part (b) to predict the value of y when x = 20. (Round your answer to two decimal places.) Please be as detailed as possible in the solution so i may follow along. Thank you for the help!
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.
A sample of the number of sales per hour at Store X and the number of sales at Store Y at the same times is as indicated below. Find the Y-value of the regression line where X = 5. X Y 0 1 0 2 1 2 3 4 4 6
The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.
The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old male individual is _____. a. $46,800 b. $49,800 c. $13.80 d. $13,800
Consider the following population linear regression model of individual food expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is the individual’s age, and 50+0.5X is the population regression line. Suppose we generate artificial data for 3 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Answer the following questions. Show your working. (a) What are the values of V1 and V4? (b) Suppose we know that in this artificial sample, the sample covariance between X and Y is 150, and the sample variance of X is 100. Compute the OLS regression line of the regression of Y on X. (Hint: Assume these summary statistics and the OLS regression line continue to hold in parts (c)-(e).) (c) What are the values of V5 and V7?
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.
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