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- 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?Consider the regression model Yi = β0 + β1X1i + β2X2i + ui. Transform the regression so that you can use a t-statistic to testa) β1=β2.b) β1+aβ2=0.c) β1 + β2 = 1.Suppose you have the following data: X Y 3 9 7 45 5 25 2 8 Using OLS methods: estimate the following regression model: Sq root of Yi = Beta0 + Beta1(Xi) + error
- Past 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.consider a regression model Yi=B1+B2Xi+ui and you estimated B2hat =0.3. This implies that a unit change x is prdicted toGiven the regression equationY = 43 + 10Xa. What is the change in Y when X changes by +8?b. What is the change in Y when X changes by -6?c. What is the predicted value of Y when X = 11? d. What is the predicted value of Y when X = 29? e. Does this equation prove that a change in X causes a change in Y?
- Consider the regression model Yi = b0 + b1X1i + b2X2i + ui. Use approach 2from Section 7.3 to transform the regression so that you can use a t-statistic to testa. b1 = b2.b. b1 + 2b2 = 0.c. b1 + b2 = 1. (Hint: You must redefine the dependent variable in theregression.)An OLS regression should be used when the independent variable is nominal. A. True B. FalseDEPENDENT VARIABLE Qc R- SQUARE P- VALUE ON F 64 0.8093 0.0001 INDEPENDENTVARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 10. Write the resulting regression equation. Q = f( P, M, PR) where Qc = demand for cement/month (in yards) Pc = the price of cement per yard, M = country’s tax revenues per capita, and PR = the price of asphalt per yard.
- 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 the IV regression model Yi = β0 + β1Xi + β2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept (The IV Regression Assumptions) are satisfied. Which IV assumption is not satisfied whena) Zi is independent of (Yi, Xi, Wi)?b) Zi=Wi?c) Wi is1 for all i?d) Zi=Xi?Interpret the coefficients in the regression model