3. The following model is proposed for a set of variables. y = Bo+ B1X1 +...
3. The following model is proposed for a set of variables. y = βο + βιX1 + β2Χ2 + β3Χ3 +ε Based on the following correlation matrix, what potential problem is there? Why? Correlations: y, x1, x2, x3 x2 x1 32 -0.825 0.000 0.829 0.000 -0.718 0.000 -0.978 0.000 0.936 0.000 -0.904 0.000 Cell Contents: Pearson correlation P-Value
Q.28 Suppose you perform the following multiple regression: Y = B0 + B1X1 + B2X2 + B3X3. You find that X1 and X3 have a near perfect correlation. How would you conclude on the utility of your regression result? a. This is a problem of multicollinearity which renders the entire regression invalid. b. This is a problem of multicollinearity which nevertheless does not necessarily invalidate the utility of the model as a whole. c. This is NOT a regression problem...
1. A professor examined the relationship between the number of hours devoted to reading, each week Y and the independent variable social class X1), the number of years of school completed x2 and reading speed X3, in pages read per hour. The following ANOVA table obtained from a stepwise regression procedure for a sample of 19 women over 60. A) Fill in the missing values. DESS Source Regression x3 MS P value 1 1058.628 Residual 585.02 Regression X2 X3 183.743...
Consider the regression model y = Bo + B1X1 + B2X2 + ε where Xy and X2 are as defined below. Xq = A quantitative variable 1 if x2 <20 x2 = { 0 if X, 220 The estimated regression equation ý = 23.9+ 5.4x4 +6.9x, was obtained from a sample of 20 observations. Complete parts a through d below. a. Provide the estimated regression equation for instances in which X4 <20. y=1( ) x (Type integers or decimals.) b....
Question 2: Indicate whether each of the following statements is true or false and explain concisely why. 1. The Frisch-Waugh-Lovell theorem states that in a multiple linear re- gression Y = Bo + B1X1 + B2X2 + B3X3 + B4X4 +U, the estimate 1 we get for B1 is what we would have obtained by regressing Y on "the part of Xị that has nothing to do with X2, X3, X1, and U.
A nutritionist wants to model the relation between calories, protein, fat, and carbohydrates in breakfast cereal. Using a random sample of 12 ready-to-eat breakfast cereals, she obtained the following data per 100g of cereal Protein(g) Fat(9) Carbohydrates(9) 89 83 88 81 81 Calories 373 380 389 370 355 381 357 387 347 385 386 377 87.1 3.8 4 3 93.7 10 3.2 32 - 3.4 3.2 9.1 5.5 6.4 1.8 7.9 1.8 3.6 3.9 6.4 3.6 6 1 73 89...
Assume that the variable Y is actually determined by the following equation Y; = Bo + B1X1,i+ B2X2,i + Uj additionally assume that corr(X1, X2) = p. The usual assumptions for a linear model hold in this case. You are interested in estimating B1. To accomplish this you collect a sample of the variables Y and X1 and estimate the following model Y; = Yo + 91X1,i+ vi (3) Answer the following questions 6. If p= 0 and B2 >...
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual i's University GPA and xi is the individual's high school grades. a. What do you think is in ui? Do you think E[ulx) = 0? Suggest a variable that you think might affect University GPA that isn't included in the regression equation but should be. c. What sign of bias would you expect in an OLS regression of y on x? Briefly explain. d....
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: 0.04 + 0.28X1 + 0.84X2-0.06x3 + 0.14x4 y She would like to conduct significance tests for a multiple regression relationship. She uses the F test to determine whether a significant relationship exists...