Question

Correlation and Regression Analysis

Question 2                 

The marks in a Physics exam (P) and a Chemistry exam (C) were recorded for 15 students:

Physics	25	46	63	45	78	18	84	48	73	50	61	89	38	36	30
Chemistry	31	44	58	49	66	12	61	56	70	57	62	56	29	40	38

1. Draw a scatter diagram and comment.
2. Find the regression line where the Chemistry mark is the explanatory variable and the Physics mark is the response variable.
3. Calculate the correlation between P and C. Test the hypothesis, at 5%, that it is positive.
4. Predict the Physics mark of three students, one obtaining 20 in Chemistry, one 50 in Chemistry and the third 80 in Chemistry. Which of the three predictions do you trust more?
5. Perform a hypothesis test that the slope of the regression line is positive.

Answer 1

a)

b)

Physics = -3.5621 + 1.1487 * Chemistry

c)

correlation between P and C r = 0.8465, Positive and Strong correlation between P and C

Hypothesis:

H0: ρ = 0

Ha: ρ > 0

Test:

t = r * SQRT((n-2)/(1-r^2)) = 0.8465 * SQRT((15-2)/(1-0.8465^2)) = 5.733

P value = 0.0001 (alpha = 0.05, df = n-2 = 13)(Use t table)

P value < 0.05, correlation between P and C is positive at 5% significance level

d)

Physics = -3.5621 + 1.1487 * Chemistry

If Chemistry = 20

Physics = -3.5621 + 1.1487 * 20 = 19.4119

If Chemistry = 50

Physics = -3.5621 + 1.1487 * 50 = 53.8729

If Chemistry = 80

Physics = -3.5621 + 1.1487 * 80 = 88.3339

e)

Slope b1 = 1.1487, SE = 0.2004 (From the excel output)

Hypothesis:

H0: β1 = 0

Ha: β1 > 0

Test:

t = b1/SE = 5.7319 (from the excel output)

P value = 0 (T.DIST.RT(ts,DF)) (DF = n-k = 13)

P value < 0.05, Reject H0

Therefore, the slope of the regression line is positive at 5% significance level