Question 5

Use the dataset provided to examine how firms' stock returns (y) are affected by different independent variables using multiple linear regression models. There are 4 independent variables, including firms' PE ratio (denoted as pe), firms' dividend payment (denoted as dividend), firms' revenue amount (denoted as revenue), and firms' industry (denoted as industry). Each row of data represents the observation of a stock in the sample.

Create two dummy variables. The first dummy variable denotes the high revenue firm. If firm's revenue is greater than or equal to 2 million, then the firm has high revenue, and its first dummy variable is equal to one. If firm's revenue is less than 2 million, the firm has low revenue, and its first dummy variable is equal to zero. The second dummy variable denotes the materials firm. For the firm whose industry is materials, the second dummy variable is equal to one. For the firm whose industry is non-materials, the second dummy variable is equal to zero.

1. Run the multiple linear regression without dummy variables interaction (i.e. the four independent variables are x1, x2, and two newly created dummy variables). Please write the regression equation below.

1. Analyze the summary of regression results (i.e. state the estimated values of regression coefficients, interpret the use of R-squared, determine if each population regression coefficient is different from zero by using t-value or P-value. Interpret if the high revenue firms' stock returns are different from low revenue firms, and if the materials firms' stock returns are different from non-materials firms). Use 10% as the significance level.

1. Run the multiple linear regression with dummy variables interaction (i.e. the five independent variables are x1, x2, two newly created dummy variables and their interaction term). Please write the regression equation below.

1. Interpret if the dummy variables interaction exists

1. Screenshot the code and results.

return	pe	dividend	revenue	industry
0.05	2	4	12003300	materials
0.13	2	3.35	12420000	materials
0.01	4	4	2533653	non-materials
0.08	3	3.6	132000	materials
0.11	5	3.45	606536.4	materials
0.15	6	3.25	1573199	materials
0.17	8	3.15	175692	materials
0.01	5	4	2533653	non-materials
0.22	9	2.9	212587.3	materials
0.23	10	2.85	2303321	materials
0.22	9	3	257230.7	materials
0.05	12	3.75	212587.3	non-materials
0.29	16	2.55	455699.8	materials
0.33	14	2.35	311249.1	materials
0.33	13	2.35	7228808	materials
0.35	16	2.25	414272.5	materials
0.11	17	3.45	455699.8	non-materials
0.39	17	2	501269.8	materials
0.41	18	2	212587.3	materials
0.22	20	2.9	2303321	materials
0.45	18	1.75	667190.1	materials
0.22	22	2.9	733909.1	non-materials
0.22	23	2.9	807300	materials
0.55	24	1.25	888030	materials
0.51	25	1.45	212587.3	materials
0.33	22	2.35	1074516	non-materials
0.33	27	2.35	1181968	materials
0.59	28	1.05	1300165	materials
0.61	33	0.95	1430181	materials
0.66	26	0.7	233846.1	materials
0.44	31	1.8	1730519	non-materials
0.67	33	0.65	1903571	materials
0.66	33	0.7	2093928	materials
0.71	34	0.45	212587.3	materials
0.73	33	0.35	3372292	materials
0.77	36	0.15	1573199	materials
0.77	37	0.15	3065720	materials
0.79	36	0.05	4488521	materials
0.83	39	0	132000	materials
0.66	37	0.7	4080474	non-materials
0.85	41	0	4488521	materials
0.87	44	0.01	4937373	materials
0.88	43	0.05	212587.3	materials
0.77	44	0.15	3709522	non-materials
0.83	45	0.05	65712644	materials
0.95	44	0.05	7228808	materials