.relationship between hours studied to the test scores. predict the test score if a student studied 4.5 hours. s.

Question

Hours Studied     Test Score

  135.8                      6167        there are 24 rows for each        

ave 5.658                 256.958

 

   
Coefficient  (b1)
-98.944374
816.8186
Intercept Coefficient  (b0)
 
Standard Error
38.748297
219.4388
Intercept Standard Error
 
R Square
0.2286234
44.49029
Standard Error
 
 
F
6.5204411
22
Residual df
 
 
Regression MS
12906.469
43546.49
Residual MS
    

Answer 1

Donna,

 

Use the 24 pair of values (x,y) where x denotes the number of hours spent and y represents the score, to find the equation of the regression line of the form: y = mx + b, where m is the slope of the line and b is its intercept. Note that this can be done in Excel in a number of different ways. One way is to enter the given hours spent in one column, say column A; and the y values in another column (e.g., column B). Next, choose any cell and type in:  =SLOPE(y data , x data) to obtain the value for m (the slope). For finding the intercept b, choose another cell and type in: =INTERCEPT(y data , x data). once you have determined the values for m and b, then write the equation y=mx+b, and plug in 4.5 for x in the above equation in order to calculate the predicted y value.

 

Note 1: If the given 24 values of x occupy cells A1 to A24, then the "x data" should be entered into the both formulas as: A1:A24. Similarly, if the given 24 values of y occupy cells B1 to B24, then the "y data" should be entered into the both formulas as: B1:B24 ; that is:

=SLOPE(B1:B24 , A1:A24),  and   =INTERCEPT(B1:B24 , A1:A24)

 

Note 2: The values that you have included for slope (your b1) and the intercept (your b0) do not make sense and seem to be incorrect. Furthermore, we expect the coefficients of correlation and determination to be relatively large for this situation. By "large" we mean that their values are close to 1 (such as 0.9 or 0.8). However, your value of R-squared (Coeff. of determination) is about 0.22 which is really too low and indicates a very weak correlation between hours spent and grade gained.

 

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