Question

In: Statistics and Probability

1. A statistics instructor at a Sultan aboos University would like to examine the relationship between...

  1. 1. A statistics instructor at a Sultan aboos University would like to examine the relationship between the number of optional homework problems students do during the semester and their course score. She randomly selects 10 students for study and asks them to keep track of the number of these problems completed during the course of the semester.

Course Score (x)

No. of Problem (y)

15.2

225

17.4

335

12.9

195

16.2

342

19.5

416

23.1

532

20.4

422

26.1

624

24.4

554

19.1

434

  1. Calculate the coefficient of correlation between x and y and comment on the result.
  2. Calculate the coefficient of determination and interpret the result.
  3. Test the hypothesis at the 5% level of significance that there is no association between the Course Score and No. of Problem.
  4. If we apply Simple linear regression to the above data, will it give same results of correlation?
  5. How you can identify the difference between correlation and regression?

Solutions

Expert Solution

a) From the given data

b) Correlation Deterimination r2 = 0.98372 = 0.9676

i.e. 96.76% of variation in the No. of problem is explained by the Course score (X)

c) Test for correlation coefficient:

Thus we conclude that there exist correlation or association between Course Score (x) and No. of Problem (y)

d) Regression Equation:

e) Correlation measure how much the relationship between Course Score (x) and No. of Problem (y) exist but regression equation is used to predict the Y values for various x values are know with the correlation coefficient

orchestra answered 2 years ago
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