Question

A statistics professor believes that the amount of time a student spends studying is predictive of their test scores. The professor obtains study time (in hours per week) and test grades from a random sample of 9 students. The data is presented in the table below: Hours Spent Studying Per Week Test Scores 11 80 2 37 1 14 4 66 3 43 5 52 7 96 6 51 3 44

ΣX=

ΣX2=

ΣY=

ΣY2=

ΣXY=

1A. Create the regression equation that predicts test scores based on hours spent studying per week.

1B. What is the value of the y-axis intercept for the regression equation?

1C. Suppose a student studies 6 hours per week. Estimate what their test score will be.

1D. For each unit increase in hours studied (1 hours), how many points do you predict the test score would increase?

Answer 1

X	Y	XY	X²	Y²
11	80	880	121	6400
2	37	74	4	1369
1	14	14	1	196
4	66	264	16	4356
3	43	129	9	1849
5	52	260	25	2704
7	96	672	49	9216
6	51	306	36	2601
3	44	132	9	1936

	X	Y	XY	X²	Y²
total sum	42.000	483.000	2731.00	270.000	30627
mean	4.6667	53.6667

sample size ,   n =   9          
here, x̅ =Σx/n =   4.6667   ,   ȳ = Σy/n =   53.66666667  
                  
SSxx =    Σx² - (Σx)²/n =   74.000          
SSxy=   Σxy - (Σx*Σy)/n =   477.000          
SSyy =    Σy²-(Σy)²/n =   4706.000          
estimated slope , ß1 = SSxy/SSxx =   477.000   /   74.000   =   6.4459
                  
intercept,   ß0 = y̅-ß1* x̄ =   23.5856          
                  
so, regression line is   Ŷ =   23.5856   +   6.4459   *x

...........

B)

intercept,   ß0 = y̅-ß1* x̄ =   23.5856      

...........

C)

Predicted Y at X=   6   is                  
Ŷ =   23.586   +   6.446   *   6   =   62.261

........

D)

For each unit increase in hours studied (1 hours), 6.4459 POINTS would increase

..............

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