In: Statistics and Probability

**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 |

- Draw a scatter diagram and comment.
- Find the regression line where the Chemistry mark is the explanatory variable and the Physics mark is the response variable.
- Calculate the correlation between P and C. Test the hypothesis, at 5%, that it is positive.
- 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?
- Perform a hypothesis test that the slope of the regression line is positive.

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

2. Describe the difference between correlation and prediction
(regression) analysis approaches?

How is a linear regression analysis is different from a
correlation analysis?

Discussion Prompt 2: Correlation and
Regression
Correlation and regression are two important terms in
statistics. Select an area that interests you and use it to answer
the following:
Explain the difference between correlation and regression using
examples
Explain the different types of regression using examples

If I receive STATA output (regression) in an exam, and the
question is to detect the following issues:
1- Heteroscedasticity
2- multicollinearity
3- Omitted variable
3- over specification
How can I detect them and know and detect there is issue in this
output easily?
for example I know one of the signs of multicollinearity issue
is when I notes insignificant t-values.

True or False: Regression analysis is used for
prediction, while correlation analysis is used to measure the
strength of the association between two numerical
variables.
A. True
B. False
In performing a regression analysis involving two
numerical variables, we are assuming
A. the variances of X and Y are equal.
B. the variation around the line of regression is the same for
each X value.
C. that X and Y are independent.
D. All of these.
Which of the following...

Explain the difference between correlation analysis and
regression analysis. Give an example of a lurking variable. If a
statistician computed a value of r = -2.83 what would you tell that
statistician? Under what circumstances can we calculate r? Can the
regression equation be assumed to hold 100 years from now? Are
there other correlation coefficients other than the Pearson Product
Moment Correlation Coefficient

QUESTION 2
(This question comes from the OCT/NOV 2018 exam)
Terry’s Chocolates has been supplying the South African market with
quality chocolates and chocolate products since 1987. The
organisation manufacturers a range of confectionery and has an
extensive range of products. A consulting company was hired in
order to carry out a strategic review of Terry’s. Terry’s Board of
Directors also requested that the consulting company should suggest
alternative strategies for achieving growth. Following the review
Terry’s management will make...

Question 7. The results of the correlation
analysis in the Correlation Matrix these variables
are depicted below. Use information in the table to discuss the
strength and nature of relationship between the four variables.
Training
Performance
Years of Service
Annual Salary
Training
1
Performance
0.016
1
Years of Service
0.377
-0.268
1
Annual Salary
0.597
0.709
0.286
1
Question 9. Results of the three goodness of
test measures is given in the table below:
Goodness of Fit Tests
R Square...

Question C [SD1: 5 Marks]
A multiple regression analysis between yearly income (Y in
$1,000s), college grade point average (X1), age of the
individuals (X2), and the gender of the individual
(X3; zero representing female and one representing male)
was performed on a sample of 10 people, and the following results
were obtained.
Coefficients
Standard Error
Intercept
4.0928
1.4400
X1
10.0230
1.6512
X2
0.1020
0.1225
X3
-4.4811
1.4400
ANOVA
DF
SS
MS
F
Regression
360.59
Residual...

6. Question
6 [Total: 20 marks]
Please discuss how “variation margin” and “margin call” are
related in the context of daily settlement
procedure.
[10 marks]
b) What are the most important aspects of the design of a new
futures contract?
[10 marks]

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