##### Question

In: Statistics and Probability

# Correlation and Regression Analysis Question 2                  (6 marks) The marks in a Physics exam (P) and...

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.

## Solutions

##### Expert Solution

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

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