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- An independent variable in a model is also called:a. explained variable.b. unexplained variable.c. explanatory variable.d. dependent variable.Consider the regression model Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) +ui. a. ΔY>/ΔX1 = β1 + β3X2 (effect of change in X1, holding X2 constant).b. ΔY/ΔX2 = β2 + β3X1 (effect of change in X2, holding X1 constant).c. If X1 changes by ΔX1 and X2 changes by ΔX2, then ΔY =(β1+β3X2)ΔX1 + (β2 + β3X1)ΔX2 + β3ΔX1ΔX2.Consider the regression model Yi = β0 + β1Xi + ui.a. Suppose you know that β0 = 0. Derive a formula for the least squaresestimator of β1.b. Suppose you know that β0 = 4. Derive a formula for the least squaresestimator of β1?
- Find the degrees of freedom in a regression model that has 10 observations and 7 independent variablesIf in a regression, there are many variables, two of them show a square relationship (for example, A and A^2), A and A^2 show a strong positive correlation. Is there any problem with the model specificationPast class data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from the College of Information Technology and Engineering from Dr. Kalaw is: final exam = 50 + 0.5 × midterm One interpretation of the slope is a. students only receive half as much credit (.5) for a correct answer on the final exam compared to a correct answer on the midterm exam. b. a student who scored 0 on the midterm would be predicted to score 50 on the final exam. c. a student who scored 10 points higher than another student on the midterm would be predicted to score 5 points higher than the other student on the final exam. d. a student who scored 0 on the final exam would be predicted to score 50 on the midterm exam.
- Suppose you run the following regression: outcome=alpha0 + alpha1*female + alpha2*married + epsilon. You know that female equals 1 for females and 0 otherwise. You know that married equals 1 if the person is married and 0 otherwise. What is the estimated outcome for non-married respondents who are not female?Given the regression equation Y = 100 + 10X a. What is the change in Y when X changes by +3? b. What is the change in Y when X changes by -4? c. What is the predicted value of Y when X = 12? d. What is the predicted value of Y when X = 23? e. Does this equation prove that a change in X causes a change in Y?Suppose you run the following regression: outcome=alpha0 + alpha1*female + alpha2*married + epsilon. You know that female equals 1 for females and 0 otherwise. You know that married equals 1 if the person is married and 0 otherwise. What is the estimated outcome for married respondents who are not female?
- True or False For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable.Consider the simple linear regression model given by E(y) = 1.5 + 0.23*x where y is measured in litres and x is measured in dollars. What must be the value of the slope coefficient if x is measured in thousands of dollars while the unit of measurement of y is unchanged (i.e., x is divided by 1000)? Answer:Consider a data set with 15 observations and consider a multiple linear regression model with 7 in-dependent variables. Assume you have estimated the model and you find that SST = 1,325 and SSR = 794.