A researcher is using data for a sample of 25 business schools that offer MBA degrees...

 

Transcribed Image Text:

A researcher is using data for a sample of 25 business schools that offer MBA degrees to investigate the relationship between the annual salary gain of graduates Y, (measured in thousands of dollars per year) and annual tuition fees X, (measured in thousands of dollars per year). Preliminary analysis of the sample data produces the following sample information: N= 25 EY, = 1,034.97 Ex, =528.599 £Y? = 45,237.19 N N N Ex = 11,432.92 Ex,Y, = 22,250.54 Ex,y, = 367.179 %3D N Eyi =2,390.67 Ex = 256.241 E = 526.147 where x, = X, - X, y, = Y, - Y and y, = Y, -Y for i = 1, ., N. Use the above sample information to answer all the following questions. Show explicitly all formulas and calculations. (10 marks) (a) Use the above information to compute OLS estimates of the intercept coefficient B, and the slope coefficient B,. (6 marks) (b) Interpret the slope coefficient estimate you calculated in part (a) -- i.e., explain in words what the numeric value you caleulated for B, means. (6 marks) (c) Calculate an estimate of o, the error variance. (6 marks) (d) Compute the value of R', the coefficient of determination for the estimated OLS sample regression equation. Briefly explain what the calculated value of R' means. (6 marks) (e) Compute the estimated variance of B, and the estimated standard error of B. A researcher is using data for a sample of 25 business schools that offer MBA degrees to investigate the relationship between the annual salary gain of graduates Y, (measured in thousands of dollars per year) and annual tuition fees X, (measured in thousands of dollars per year). Preliminary analysis of the sample data produces the following sample information: N= 25 EY, = 1,034.97 Ex, =528.599 £Y? = 45,237.19 N N N Ex = 11,432.92 Ex,Y, = 22,250.54 Ex,y, = 367.179 %3D N Eyi =2,390.67 Ex = 256.241 E = 526.147 where x, = X, - X, y, = Y, - Y and y, = Y, -Y for i = 1, ., N. Use the above sample information to answer all the following questions. Show explicitly all formulas and calculations. (10 marks) (a) Use the above information to compute OLS estimates of the intercept coefficient B, and the slope coefficient B,. (6 marks) (b) Interpret the slope coefficient estimate you calculated in part (a) -- i.e., explain in words what the numeric value you caleulated for B, means. (6 marks) (c) Calculate an estimate of o, the error variance. (6 marks) (d) Compute the value of R', the coefficient of determination for the estimated OLS sample regression equation. Briefly explain what the calculated value of R' means. (6 marks) (e) Compute the estimated variance of B, and the estimated standard error of B.