REGRESSION ANALYSIS

Regression Analysis

Regression Analysis

Section A

Q 1. Using the One-way ANOVA,

Test the hypothesis that the variances in the regions' profitability (ROA) are equal.

ANOVA helps in predicting the relation between variable groups towards the dependent variable (ROA) based on coherent properties of the independent variable (Region) (Creswell, 2009). Thus, ANOVA statistical measurement method can be performed on each group to find out that variances in the regions' profitability (ROA) are equal or not. Null and alternate hypothesis for the test is given below.

Null hypothesis:

Ho = µ1 = µ2 = µ3

There is no statistically significant difference between average ROA of Asia, Europe, and North American region.

Numeric form: µ (Average ROA of Asian Region) = µ (Average ROA of European Region) = µ (Average ROA of North American Region)

Alternate hypothesis:

H1 = µ1 ? µ2 ? µ3

There is statistically significant difference between average ROA of Asia, Europe, and North American region.

Numeric form: µ (Average ROA of Asian Region) ? µ (Average ROA of European Region) ? µ (Average ROA of North American Region)

Descriptive statistics of the ANOVA are presented in the below table. However, main important column in the data are first and significance column. Main notable thing to note is that sum of squares for the data is higher for the within groups as compare to between groups. Between Groups represent the 1336.92 sum of squares out of 68991.43; whereas, Within Groups constitute 67654.51 sum of square value in total proportion of variance. F-value stood at 9.357, which is significant at 95% confidence interval level (p < 0.05). This shows that ANOVA test for the two selected variables result in rejecting the null hypothesis and accepting the alternate hypothesis, which states that variances in the regions' profitability (ROA) are not equal.

ANOVA

Return on Asset

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

1336.921

2

668.460

9.357

.000

Within Groups

67654.505

947

71.441

Total

68991.426

949

Is there evidence to suggest that the mean profitability of each region is significantly different from the others? Explain.

Above test define that variances in the regions' profitability (ROA) are not equal for all regions. This represents that average profitability of some regions differ significantly from other region's ROA. In order to assess the regions that have unequal variance, post-hoc Tukey test is conducted on the data to determine the unequal relation between regions with respect to the ROA. Table presented below shows the post hoc Tukey test analysis. Significance values highlighted in bold shows that relations do not satisfy the null hypothesis relation.

Therefore, at 0.05 alpha levels, we can conclude that mean profitability (ROA) of Asian and European region is not equal (p=0.0005). Similarly, mean profitability (ROA) is not equal for Asian and North American region at 0.05 alpha levels (p=0.004), resulting in rejecting the null hypothesis (Jackson, 2008).

Multiple Comparisons

Return on Asset

Tukey HSD

(I) Region

(J) Region

Mean Difference (I-J)

Std. Error

Sig.

95% Confidence Interval

Lower Bound

Upper Bound

Asia

Europe

-2.2156568*

.5846574

.000

-3.588081

-.843233

North America

-2.8656486*

.8928480

.004

-4.961518

-.769779

Europe

Asia

2.2156568*

.5846574

.000

.843233

3.588081

North America

-.6499918

.8933058

.747

-2.746936

1.446953

North America

Asia

2.8656486*

.8928480

.004

.769779

4.961518

Europe

.6499918

.8933058

.747

-1.446953

2.746936

*. The mean difference is significant at the 0.05 level.

Question 2: By means of multiple regression analysis, investigate the determinants of profitability (ROA) using SIZE, SHARE, LEV, LIQ and ...