2. In an experiment involving one dependent variable y and four explanatory variables₁, 2, 3 and 4, all possible regressions are fit to the data set consisting of n = 13cases. A constant term is routinely included in all models. The results are summarizesas follows:Regressors in Model Residual Sum of SquaresNone4073.61898.51359.52909.11325.886.91840.6112.1623.11303.3263.672.272.076.2110.771.8x1X2I3XAX1, X2X1, X3I1, I4I2, I3X2, X4x3, x4X1, X2, I3X1, X2, X4X1, X3, 4X2, X3, x4X1, X2, X3, X₁(a) What model will result from automatic forward selection with a significance levelof 0.1 (a to enter)? Show all your work and how you obtained this model.(b) What model will result from automatic backward selection with a significancelevel of 0.1 (a to drop)? Show all your work and how you obtained this model.(c) Compare the value of the C, statistic for the model you found in part (b) to themodel that includes all four x's.

Answered: Image /qna-images/answer/4ee8cfeb-3461-4383-9d7f-6038d2302d8f.jpg

Answered: 2. In an experiment involving one…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a regression model involving 30 observations, the following estimated regression equation was obtained.ŷ = 170 + 34x1 – 3x2 + 8x3 + 58x4 + 3x5For this model, SSR = 1,740 and SST = 2,000.The degrees of freedom associated with SSE are _____. a. 6 b. 5 c. 24 d. 19
8. For the following data: a. Find the regression equation for predicting Y from X. b. Calculate the Pearson correlation for these data. Use r and SS, to compute SS standard error of estimate for the equation. and the residual Y 3 3 6. 9. 8 4 3 7 10 9.
Consider the following data on y = number of songs stored on an MP3 player and x = number of months the user has owned the MP3 player for a sample of 15 owners of MP3 players. x y 22 485 34 748 2 81 28 581 5 117 32 728 23 445 10 128 4 61 26 476 1 35 8 121 13 266 9 126 5 141 What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) y = Is the simple linear regression model useful for describing the relationship between x and y? Test the relevant hypotheses using a significance level of 0.05. Calculate the test statistic. (Round your answer to two decimal places.) t = find the P-value for this test? (Round your answer to four decimal places.) P-value=
7. Find slop of a linear regression model for the following data: x = [1, 2, 3, 4, 5, 6, 7] z = [ 1.40, 3.78, 4.41, 4.60, 8.40, 8.64, 12.81]. -1.7 -0.5 0.5 O 1.7 CS Scanned with CamScannel
Body Fat. Where we considered the regression of percentage of body fat on nine body measurements: height, weight, hip, forearm, neck, wrist, triceps, scapula, and sup. Use the technology of your choice to do the following. a. Use the maximum- R2 criterion to obtain a regression equation for these data. b. Use the adjusted- R2 criterion to obtain a regression equation for these data. c. Use the Mallows’ Cp criterion to obtain a regression equation for these data. d. Are the regression equations obtained in parts (a), (b), and (c) the same? e. Use the analysis in parts (a), (b), and (c) to select a regression equation for these data. For the regression equation that you selected, obtain plots of residuals versus fitted values, residuals versus the included predictor variables, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the…
2. Given the partial results from a linear regression model below, a sample size of 504, and a=0.05, a. What is the F-Statistic for the overall model? b. Is it statistically significant? Model Residuals Total Degrees of Freedom 3 Sum of Squares 12000 12288 Mean Square F-Statistic
The least-square regression line for the given data is y = 0.449x - 30.27. Determine the residual of a data point for which x = 98 and y = 15, rounding to three decimal places. Temperature, x Number of absences, y OA. 28.732 B. 1.268 C. 121.535 O D. 13.732 72 3 85 7 91 10 90 10 88 98 75 100 80 8 15 4 15 5
Compute the peast -squares regression line for predecting y from x given the following summary statistics: X= 8.1 s=1.2 y=100 sy= 15 r= 0.70
Let sale denote the sale price for a house, sqft its square footage, and days the number of days that it has been on the market. Consider running two different regressions: First regression: sale = B1 + B2sqft + ß3days + e Second regression: sale = Bi + B2sqft + e Which of the following statements is false? In the options below, the quantities SST, SSE, and SSR are as defined when we discussed R?, that is SST = E(Y, – Ỹ)², SSE = E(Y; - Ý )², and SSR = i=1 O a. The SST from the first regression can be strictly smaller than the SST from the second regression. O b. The SSE from the first regression can be strictly smaller than the SSE from the second regression. O c. The R- from the first regression can be strictly larger than the R2 from the second regression. O d. The R2 from the second regression is equal to the R2 from the regression sqft = Yi + Y2sale + e O e. The SSR from the first regression can be strictly larger than the SSR from the second regression.
3. Regression analysis breaks scores on the DV into... (explain and give equations)

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