# Analysis of Variance (ANOVA) - F test

See the attached file.

Happy Fund's manager believes that the return on Airline shares is dependent the fluctuations in oil prices and interest rates. He collects the weekly data on the share prices, oil prices, and interest rates. Use the data provided and regression analysis and show whether oil prices and interest rate affect the returns on Airline share.

All tests should be done on 5% level of significance.

Date Airline Crude Oil Price 10-yr Interest Rate

8/1/10 13.9 78.89 3.83

15/1/10 14.42 78.65 3.7

22/1/10 13.48 75.26 3.62

29/1/10 12.8 71.99 3.63

5/2/10 13.08 72.28 3.59

12/2/10 14.12 70.42 3.69

19/2/10 13.96 73.46 3.78

26/2/10 14.42 75.98 3.61

5/3/10 14.78 76.45 3.69

12/3/10 15.32 78.17 3.71

19/3/10 15.64 77.92 3.7

26/3/10 16.16 77.6 3.86

2/4/10 16.46 78.62 3.96

9/4/10 16.52 82.57 3.9

16/4/10 15.88 83.03 3.79

23/4/10 16.7 82.24 3.84

30/4/10 16.4 83.56 3.69

7/5/10 15.18 81.71 3.45

14/5/10 15.7 76.56 3.44

21/5/10 15.02 71.17 3.2

28/5/10 15 67.91 3.31

4/6/10 15.7 70.97 3.2

11/6/10 15.54 70.68 3.24

18/6/10 15.8 73.85 3.24

25/6/10 15.9 75.09 3.12

2/7/10 15.34 73.54 3

9/7/10 15.58 71.72 3.07

16/7/10 15.62 73.49 2.96

23/7/10 16.36 73.8 3.02

30/7/10 17.28 74.69 2.94

6/8/10 18.5 78.68 2.86

13/8/10 18.9 77.28 2.68

20/8/10 19.54 73.81 2.62

27/8/10 19.14 71.28 2.66

3/9/10 19.8 73.45 2.72

10/9/10 21.4 74.42 2.81

17/9/10 21.4 76.11 2.75

24/9/10 21 75.14 2.62

1/10/10 21 76.14 2.54

8/10/10 22.1 80.89 2.41

15/10/10 21.9 80.85 2.59

22/10/10 20.95 79.35 2.59

29/10/10 20.85 79.54 2.63

5/11/10 21.65 81.96 2.58

12/11/10 22.05 85.54 2.76

19/11/10 23 82.82 2.88

26/11/10 22.7 81.17 2.87

3/12/10 23.75 84.16 3.03

10/12/10 23.4 88.18 3.32

17/12/10 22.2 88.34 3.33

24/12/10 21.55 89.43 3.32

31/12/10 21.45 90.61 3.3

7/1/11 22.45 91.04 3.34.

https://brainmass.com/statistics/analysis-of-variance/analysis-variance-anova-f-test-533145

#### Solution Preview

A Multiple Regression Analysis has been performed to analyze whether oil prices and interest rate affect the returns on Airline share. In this analysis, the dependent variable is the Airline Share. Crude Oil Price and 10-Year Interest Rate are the independent variables or predictors, which have been used for predicting the dependent variable. The Multiple Regression Analysis has been performed in EXCEL.

The regression equation is given as

y=0.795x_1 - 5.1052x_2 + 4.6815

where x_1 represents the independent variable Crude ...

#### Solution Summary

The solution discusses the analysis of variance (ANOVA) regarding the f-test.

ANOVA Problem

When we want to test two samples to determine if it is likely that the population means (estimated by the sample means) are different, we typically use a t-test. If the samples are large, we can also use a z-test. (Note that the formulas for computing s, t and/or z in the case of a two-sample test are different than the formulas for computing the same values in a one-sample test. Use Excel data analysis to conduct tests comparing two sample means.)

Using ANOVA (short for Analysis of Variance), however, we can test 3 or more sample means to determine if at least one of the sample means comes from a population with a mean that is significantly different from all of the others in the test. We actually do this by estimating a combined population variance two different ways and comparing the two estimates (the ratio of these two variance estimates follows the so-called "F distribution").

Question:

Why do we need a new test method to compare the means of 3 or more populations? Why can't we just use a series of z-tests or t-tests to compare all of the possible pairs of population means to see if one (or more) is different?

Most of the testing is to determine one or two things:

1. Is there a statistically significant difference between two or more population means? (based on comparison of 2 or more sample means)

2. Is there a statistically significant relationship between two or more variables? We can use regression analysis or chi-square tests to answer this second question.)

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