The problem is wit the high correlation among the x1, x2 and x3.
Considering x1 the correlation between y and x1 is -0.825 whereas x1 is more related to x2 ( -0.978 ) and x3 ( 0.936 ) than y. And the correlations are significant.
Similarly, considering x2 the correlation between y and x2 is 0.829 whereas x2 is more related to x1 ( -0.978 ) and x3 ( -0.904 ) than y. And the correlations are significant.
Similarly, considering x3 the correlation between y and x3 is -0.718 whereas x1 is more related to x1 ( 0.936 ) and x2 ( -0.904 ) than y. And the correlations are significant.
Hence, there is a problem of multicollinearity.
3. The following model is proposed for a set of variables. y = βο + βιX1...
3. The following model is proposed for a set of variables. y = Bo+ B1X1 + B2X2 + B3X3 + € Based on the following correlation matrix, what potential problem is there? Why? Correlations: y. x1, x2, x3 ل 0.000 0.829 0.000 -0.718 0.000 OD OOO لها 0.000 -0.904 0.000 | correlation -Va
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...
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...
Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which result in the following function: Y = 33 + 8X1 – 6X2 + 16X3 + 18X4 For this multiple regression model, there were 35 observations: SSR= 1,400 and SSE = 600. Assume a 0.01 significance level. What is the predictions for Y if: X1 = 1, X2 = 2, X3 = 3, X4 = 0
Consider a linear regression model with n predictor variables X1, . . ., Xk and a target variable y: y= β0+β1X1+…+βkXk+ε . We take n measurements of the predictor and target variables to obtain the following matrix equation: y=Xβ+εy:nx1, X:nxk+1 SSE=εTε, ε=y-Xβ Calculate the number of degrees of freedom of SSE.
You run a correlation matrix between a Y variables auto sales in units and two X variables auto prices (X1) and car buyer’s income (X2). As expected auto prices had a high negative correlation to auto sales while buyer’s income had a high positive correlation. Both X variables had significant correlations. When you run a multiple regression analysis of the forecast variable auto sales with independent variables automobile price and car buyer’s income the results were positive coefficients for both...
A regression model was constructed by regressing Y on 5 explanatory variables, X1, X2, X3, X4, and X5. There were n = 40 observations (rows) in the data set. In this case, the degrees of freedom (d.f.) for the error term in the model is:
(12 points) The random variables X1, X2, and X; are jointly Gaussian with the following mean vector and covariance matrix: 54 2 07 2 5 -1 0-1 The random variable Y is formed from X1, X2, and X; as follows: Y=X1 - X2 + X3 +4. Determine P( Y> 3).
1.The following tables give the results for the full model, as well as a reduced model, containing only experience Test Ho: ß,-Bs-0 vs HA: β2 and/or β3 # 0 Complete Model: Y-βο + β1X1 + β2X2 + β3Xs + ε ANOVA MS P-value df 76.9 Regression Residual Total 2470.4 823.5 224.7 2695.1 .0000 10.7 21 24 Reduced Model: Y = β0 + β X + ε MS df 1 23 24 value 2394.9 2394.9 183.5 0.0000 300.2 13.1 2695.1 Regression...
Consider the following three models: (a) Model 1: Y ~ X1 + X2 + X3 + X4 with AIC = -1234.3 (b) Model 2: Y ~ X1 + X3 + X5+ X7 with AIC = -1279.4 (c) Model 3: Y ~ X2 + X4 + X6 + X7 with AIC = -1189.2 Using the AIC values which model should we select as the best model?