A sample of students was taken measuring the hours studied for a test and the sc

Question

A sample of students was taken measuring the hours studied for a test and the score on the test (out of a possible total of 350 points)

X(# hours study) Y (Score on test)

5 155

7 210

8 150

10 192

11 245

13 260

15 270

18   275

20   290

a). Give the following: i) sum of the x ii) sum of the y iii) sum of the x squared iv) sum of the xy v) sum of the y squared b) Find b sub 0 and b sub 1 using the formulas in Excel that were used in the module. Round to 3 decimal places. c) Find the equation of the regression line. d) What is the value of the slope and interpret its meaning in the context of this problem e) Predict the test score for 13 hours of study. f) Calculate the coefficient of determination by writing the formula in Excel. Show your calculations. g) What % of the variation in test scores is explained by the # hours of study? h) What % is due to other factors? i) Name 1 other factor that could affect a test score. j) What is the calculated F in testing the null hyothesis: no significant relation between # hours of study and test scores. (You must use the Tool-Pak for this.) k) What is the p-value? l) Is there a significant relation between #hours of study and test scores? Please answer yes or no.

Explanation / Answer

(a)

(b)

b0=(sum(y)*sum(x2)-sum(x)*sum(xy))/(n*sum(x2)-(sum(x))2)=(2047*1477-107*26240)/(9*1477-107*107)=116.995

b1=(n*sum(xy)-sum(x)*sum(y))/ (n*sum(x2)-(sum(x))2) =(9*26240-107*2047)/(9*1477-107*107)=9.290

(c) regression equation is y=116.995+9.290x

(d) slope=9.290, this imply that unit change in x there will be 9.290 unit change in y

(e) for x=13, y=116.995+9.290*13=237.765

(f) following information has been generated using ms-excel

coefficient of determinnation=R2= 0.7979

(g) 79.79% variation is explained byt the hours of study

(h) 20.21% is due to other factor

(i) familly income or education of parents

(j)F=27.65

(k)p-value=0.0011

(l) yes, there is significant relation as p-value is less than level of signifiance alpha=0.05

X Y X2 Y2 XY 5 155 25 24025 775 7 210 49 44100 1470 8 150 64 22500 1200 10 192 100 36864 1920 11 245 121 60025 2695 13 260 169 67600 3380 15 270 225 72900 4050 18 275 324 75625 4950 20 290 400 84100 5800 sum 107 2047 1477 487739 26240

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