please help Regression Math Question 18 Please show your wor

Thirteen students entered the undergraduate business program at Rollins College 2 years ago. The following table indicates what their grade-point averages (GPAs) were after being in the program for 2 years and what each student scored on the SAT exam (maximum 2400) when he or she was in high school. Is there a meaningful relationship between grades and SAT scores? If a student scores a 1200 on the SAT, what do you think his or her GPA will be? What about a student who scores 2400?

Solution

Using technology, we get              
              
slope =    0.001142531          
intercept =    1.027770813          
              
Thus, the regression line is              
              
y^ =    0.001142531   x   +   1.027770813
                  
              
Also, getting the correlation,              
              
r =    0.691801457          

Using a table for critical values of r, as

df = n - 2 = 13 - 2 = 11

Thus, at 0.05 level,

r(Crit) = 0.553

Thus, as r > 0.553, then there is significant relationship between grades and SAT scores.

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Thus, if x =    1200
  
Then  
  
y^ =    2.398808108 [answer]

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Thus, if x =    2400
  
Then  
  
y^ =    3.769845402 [answer]