Least-Squares Method and Coefficient of Determination

The director of graduate studies at a large college of business would like to predict the grade point average (gpa) of students in an MBA program based on Graduate Management admission test (GMAT) scores. A sample of 20 students who had completed 2 years in the program is selected. The results are as follows:

(Hint: First, determine which are the independent and dependendent variables)
a.Construct a scatter plot and, assuming a linear relationship, use the least-squares method to compute the regression coeffients b(0) and b(1)

b. Interpret the meaning of the y-intercept, b(0), and the slope, b(1), in this problem.

c. Use the prediction line developed in (a) to predict the GPA for a student a GMAT score of 600

This solutions contains a graphical display of the data to determine the regression equation and the coefficient of determination. It also interprets the y-intercept and predicts the GPA for a GMAT score of 600.

The following results were obtained from a simple linear regression analysis. Total sum of square = 5.7640. Explained sum of squares = 5.5415. Unexplained sum of squares = 0.2225. The coefficient of determination is ____

The following information regarding a dependent variable Y and an independent variable X is provided.
EX = 16 E (X - X)(Y - Y) = -8
EY = 28 E (X - X)2 = 8
n = 4 SST = 42
SSE = 34
The coefficient of determination is
A. 0.1905
B. -0.1905
C. 0.4364
D. -0.4364
The coefficient of correlatio

** Please see the attached file for the complete problem description **
The solution computes for forecasting, linear equation, least-squares regression method, estimates, correlation coefficient, relationships and the coefficient of determination.

The test scores of 6 randomly picked students and the numbers of hours they prepared are as follows:
Hours: 5 10 4 6 10 9
Score: 64 86 69 86 59 87
The equation of the regression line is y(^on top)=1.06604x+67.3491. Find the coefficient of determination.

In a regression model involving 30 observations, the following estimated regression equation was obtained:
Y(hat) = 17 + 4X1 - 3X2 + 8X3 + 8X4
For this model SSR = 700 and SSE = 100.
The coefficient of determination for the above model is approximately
A. -0.875
B. 0.875
C. 0.125
D. 0.144
The c

Please help with the following sales and advertising question.
1. Regression analysis was applied between sales in ($1000) and advertising(in $100), and the following regression function was obtained: Y = 61 +4.1X Based on this regression line, if advertising is $10,000, the point estimate for sales (in dollars) is what?

The following sample observations were randomly selected.
X: 5 3 6 3 4 4 6 8
Y: 13 15 7 12 13 11 9 5
Determine the coefficient of correlation and the coefficient of determination. Interpret the association between X and Y.

The following sample observations were randomly selected.
X:
4
5
3
6
10
Y:
4
6
5
7
7
Determine the coefficient of correlation and the coefficient of determination. Interpret.