2. In an experiment involving one dependent variable y and four explanatory variables 1₁, 12, 13 and 14, all possible regressions are fit to the data set consisting of n = 13 cases. A constant term is routinely included in all models. The results are summarizes as follows: Regressors in Model Residual Sum of Squares None 4073.6 I1 1898.5 I2 1359.5 2909.1 I3 IA I1, I2 X1, X3 I1, I4 I2, I3 I2, Is 1325.8 86.9 1840.6 112.1 623.1 1303.3

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)