QUESTION 3. Multiple regression (25 marks) Total Profitability Asset Company D/E

Question

QUESTION 3. Multiple regression (25 marks) Total Profitability Asset Company D/E Sales ROE M/B Atlanta 60.60 45.40 37.00 74.00 9.90 31.30 59.10 46.00 36.70 77.80 7.70 31.10 33.30 42.50 34.20 77.70 1190 28.50 10.60 4140 29.50 74.60 10.30 28.70 45.20 37.50 72.20 13.90 32.80 42.20 34.60 71.60 12.70 29.50 44.30 33.90 77.10 10.10 32.70 57.60 47.60 33.20 73.50 1120 31.90 37.90 43.80 34.60 75.20 11.70 28.50 34.80 45.70 38.80 77.00 9.70 29.50 44.90 35.90 78.20 1170 30.50 43.80 36.80 78.20 2.50 31.40 45.50 35.70 68.00 12.10 29.40 45.70 32.60 75.60 12.10 34.10 62.1044.70 3260 75.9012.60 29.50 46.90 35.90 77.50 10.40 31.20 44.30 34.50 77.40 12.40 30.00 43.30 33.20 77.10 12.10 31.70 31.80 45.10 33.30 75.70 11.00 30.20 54.50 44.30 33.60 74.10 1130 30.50 71.20 47.10 35.80 80.60 11.00 32.70 Cleveland 31.80 Golden State Indiana LA Lakers Memphis Milwaukee Oklahoma 56.10 44.10 37.5066.00 1120 31.20 44.80 36.20 74.20 10.70 32.50 45.80 34.30 75.70 10.90 30.80 42.404.30 34.60 79.60 1110 29.50 43.60 31.60 73.60 13.40 29.50 47.80 39.30 74.80 10.30 32.60 44.00 34.00 77.00 10.60 31.40 4.50 45.60 32.30 75.40 13.00 31.10 44.10 32.00 72.70 11.70 29.90 Philadelphia Portland 75.80 Toronto HI6007 Final Exam T1 2017

Explanation / Answer

Here profitability is dependent variable and total asset, D/E, sales, ROE and M/B are independent variables.

This is the problem of multiple regression.

We have given multiple regression output.

H0 : There is no relationship between the dependent variable and all independent variables.

H1 : There is relationship between the dependent variable and all independent variables.

Assume alpha = level of significance = 0.05

The test statistic is,

T = r * sqrt(n-2) / sqrt(1-r2)

Where r = correlation coefficient = 0.8764

N = number of data pairs = 30

T = 0.8764*sqrt(30-2) / sqrt(1 – 0.87642)

T = 9.63

Now we have to find p-value for taking decision.

P-value we can find in excel.

Syntax :

=TDIST(x, deg_freedoms, tails)

Where x is absolute value of test statistic

Deg_freedoms = n-2 = 30-2 = 28

Tails = 2

P-value = 2.199E-10 = 0.0000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : There is relationship between the dependent variable and all independent variables.

We get significant result.

Profitability = -407.9703 + 4.9612*TA + 2.3749*D/E + 0.0049*Sales + 3.4612*ROE + 3.6853*M/B

Slope are :

b1 = 4.9612

b2 = 2.3749

b3 = 0.0049

b4 = 3.4612

b5 = 3.6853

If we fix D/E, sales, ROE and M/B then one unit change in TA will be 4.9612 unit increase in profitability.

If we fix TA, sales , ROE and M/B then one unit change in D/E will be 2.3749 unit increase in profitability.

If we fix TA, D/E, ROE and M/B then one unit change in sales will be 0.0049 unit increase in profitability.

If we fix TA, D/E, sales and M/B then one unit change in ROE will be 3.4612 unit increase in profitability.

If we fix TA, D/E, sales and ROE then one unit change in M/B will be 3.6853 unit increase in profitability.

Now we have to test,

H0 : Bj = 0      Vs       H1 : Bj not= 0

Where Bj is the population slope for jth independent variable.

This is the test for individual slope.

Assume alpha = 0.05

Test statistic follows t-distribution with n-2 degrees of freedoms.

We can see that,

variables

test statistic

p-value

intercept

-5.9166

0.00041

TA

3.6276

0.0013

D/E

2.9413

0.0071

sales

0.0095

0.9925

ROE

2.5711

0.0168

M/B

2.8425

0.009

We can see that only sales is insignificant variable because p-value for sales is greator than alpha.

And remaining variables are significant variables.

SO we remove sales from the model and refit the regression.

profitability

TA

0.73

D/E

0.57

sales

0

ROE

0.01

M/B

0.67

We can see that all the variables have positive sign so there is positive relationship between profitability and TA, D/E, ROE and M/B.

And there is no relationship between profitability and sales because correlation coefficient between them is 0.

variables

test statistic

p-value

intercept

-5.9166

0.00041

TA

3.6276

0.0013

D/E

2.9413

0.0071

sales

0.0095

0.9925

ROE

2.5711

0.0168

M/B

2.8425

0.009

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.