Consider the regression of salaries (Y) on tuition fees paid (X). Following information was obtained for a sample of 22 colleges. Both X and Y are measured in $'000.
Cov(x,y)=84;?yi=1386;?xi=748;?(xi?x¯)2=2205;?(yi?y¯)2=4725;?(yhat?y¯)2=3591
Estimate the model Y=a+bX
2. Find the value of a.
Consider the regression of salaries (Y) on tuition fees paid (X). Following information was obtained for...
2. Changing Units Suppose we estimate a standard OLS regression equation on data X and Y and have the standard formulas: 3, L2=(X - X)(Y - Ý) 1=1(X; - X)2 Bo =Ỹ – BX Now suppose that Xi = 1+1.6Z; for some Zi. I.e., suppose that X; were generated by trans- forming some Zi. a) Show that: X = do +ajz for some do, ai (that you need to solve for). b) Plug in the expression from (a) into (X;...
In a simple linear regression, the following information is given: x−x− = −39; y− y− = 40; Σ(xi−x− )(yi− y−)= −840;Σ(xi−x− )(yi− y−)= −840; Σ(xi− x−)2= 718Σ(xi− x−)2= 718 a. Calculate b1. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) b1 b. Calculate b0. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) b0 c-1. What is the sample regression equation? (Negative value should be...
3) Consider the following linear regression: y =a + Bx + Show that minimizing the sum of squared residuals ( - ) to obtain OLS estimators of the slope and the intercept results in the following algebraic properties a) b) Ex = 0 = 0 4) You run the following regression: TestScore = a + (Female) + where TestScore is measured on a scale from 400 to 1000, and female is an indicator for the gender of the student. You...
1. Consider the following regression model: Y; = Bo + B1 * Xi + Ei S&x=21 SSTx = 10, SST = 90, R2 = 0.6 n = 11 x= 10, y = 30 Where y = output in pounds and x is the amount of labor used measured in hours. a. Estimate a 95% confidence interval for ß, . What is the interpretation of this confidence interval?
The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration. GPA 2.6 3.4 3.6 3.1 3.4 3.1 Monthly Salary ($) 3,500 3,800 4,200 3,800 4,100 2,500 The estimated regression equation for these data is y 914.5 854.8x and MSE 360,484. a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal). b. Develop a 95% confidence interval...
The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration. GPA 2.7 3.5 3.7 3.2 3.4 2.7 Monthly Salary () 3,500 3,900 4,200 3,700 4,100 2,500 The estimated regression equation for these data is y-313.6+1,238.6x and MSE-141,222 a. Developa point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal) b. Develop a 95% confidence interval for the mean sta...
The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration. GPA 2.6 3.4 3.7 3.1 3.5 2.9 Monthly Salary (S) 3,600 3,800 4,200 3,700 4,100 2,500 The estimated regression equation for these data is y- 564.3 +964.3x and MSE-268,482. a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal). b. Develop a 95% confidence interval for...
The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration GPA 2.7 3.4 3.7 3.1 3.4 2.9 Monthly Salary ($) 3,500 3,800 4,300 3,800 4,200 2,300 The estimated regression equation for these data is y- -726.5 1,367.6x and MSE 335,772 a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal) b. Develop a 95% confidence interval...
11. Consider the following set of n-6 observations of x and y given in Table 1 i. Graph the observations in a scatter plot on paper by hand by plotting x on the x-axis and y on the y-axis. Comment on the relationship. Using observations from Table 1, what are the sample means i and-? Using observations from Table 1, calculate the deviations and squared deviations from the sample mean for x: (x 11. iii. -x) and (x )for each...