Question

***Use R/STATA to perform the following analysis

Data: ShareValue.xlsx contains data on N=309 firms which sold new shares. Data on the following variables is provided. All variables are measured in millions of US dollars. ShrVal is the dependent variable and the all the remaining variables are the explanatory variables.

ShareValue: the total value of all shares outstanding, calculated as the price per share times the number of shares outstanding.

FirmDebt: firm’s long-term debt

TotalSales: sales of the firm.

Net_Income: net income of the firm.

TotalAssets: book value of the assets of the firm

1. Undertake appropriate basic data analytics to motivate the regression model above.

2. Using the dataset provided, run the above described regression model and interpret all regression coefficients.

3. Do you suspect any multicollinearity problem could affect the regression coefficients?

5. Use graphical method or a test of heteroscedasticity to check for evidence of heteroscedasticity in part 2.

6. Test the following hypothesis:

(a)     Is your regression model a significant predictor of share value variations for the sample of firms you are given?

(b)     Test that increasing sales by 20 million dollars, everything else held constant, would raise the share value by at least 5 million dollars;

(c)      Test the fact that jointly, a firm’s total assets and its outstanding debts better left out of this regression (Beta_TotAssets = Beta_Debt =0)

Use the Breusch-Pagan test to see if there is heteroskedasticity in this regression.

Use the White test to see if there is heteroskedasticity in this regression.

You should have found that heteroskedasticity is present. Using the strategy for "Log transforming the Model" investigate whether using a “double-log model” fixes the heteroscedasticity problem? For your transformed regression, state how the coefficients should be interpreted.

Does dividing the original (“levels”) model’s all variables by the FirmDebt variable fix the heteroskedasticity problem? For your transformed regression, state how the coefficients should be interpreted.

Using heteroskedasticity consistent estimator (HCE or White robust estimator). Estimate the regression model using one HCE.

Of the regressions in questions 9, 10, 11, which would you use as your preferred specification for inclusion for this particular project?

ShareValue	FirmDebt	TotalSales	Net_Income	TotalAssets
110.8	0.4	0.1	-5.9	11.8
52.7	0.3	57.6	1.3	13.4
108.8	0.4	7.6	-8.4	14.3
26.9	4.7	27	0.3	10.8
94	72.2	163.7	3.7	131.5
252.2	4.4	82.2	4.6	16.5
42.8	2.2	44.1	1.4	24.5
42.5	13	78.9	2.8	46
81.5	128.5	157.7	-0.2	190
472.3	283.9	1619.3	9.2	743.5
768.8	425	633.6	23.2	783.1
138.9	1.5	297.3	5.6	92.7
380.6	47	144.2	28.1	118
240	6.1	0.6	-3.7	12.9
158.2	0.6	1.4	-5.2	11.2
102.9	0.3	7.4	-3.1	7.1
69.3	20.4	102.4	1	64.6
59.4	2.4	33.8	2.5	27.3
72.2	0.2	68	9.4	44.6
28.4	2.6	13.2	0.5	9.9
287.8	0.5	23	0.6	21.1
260.8	16	63.3	7.6	47.7
82.8	7.2	96.8	6.3	49.8
18	1.6	9.3	1.3	7
52.5	0.5	35.8	0.6	5.1
62.5	0.2	54.9	2.8	18
75.6	0.5	16.5	0.3	17.5
77.2	0.6	10	-2.1	5.4
71.3	35	6.6	0.8	53.1
41.7	0.1	2.3	-1.5	2.5
205.6	9.8	161.5	10.1	58.8
2623.4	968.3	175.9	-61	658.9
57.7	0.4	0.6	-6.4	5.9
59.6	0.1	0.3	-2.8	1
94.1	0.4	0.1	-3.3	4.7
163.5	1	16.7	-6.4	26.8
64	13.4	710.8	5.3	92.9
122.9	7	20.8	1.6	28.3
144.7	2.2	413.7	7.7	94.6
21.8	0.3	2.8	0.6	1.2
199.2	238.3	27.7	5	525.2
186.4	1.3	92.6	7.6	122.8
55.8	0.1	14.2	1.2	7.9
304.8	2.5	0.3	-6.4	15.7
13.7	0.2	21.9	0.9	9.1
17.6	1.3	13.6	1.2	4.7
112.3	2.5	30.2	-0.9	13
166.6	1.4	5.5	-3.7	28.1
108.1	0.7	11.1	-0.3	4.5
147.5	0.1	16.7	1.2	10
545.8	376.1	667.2	14.9	668.3
173.4	5.3	93.5	4.7	103.2
32.5	4	36.8	1.9	22.6
61.5	0.2	30	-1.8	15.9
92.2	0.3	6.7	-3.6	5.7
39.6	0.6	17.7	1.4	2.9
24.8	0.6	5.5	0.5	5
21.4	1.9	13.1	0.6	7.4
96.8	4	28.7	-0.3	57.6
68.9	5.5	26.9	0.3	21.6
120.6	14.6	119.5	-0.2	106
234.4	111.8	38.1	-10.7	139.8
152.1	18.1	113.5	6.1	79.4
42.2	1.1	84.3	0.9	28.2
64.8	0.2	46.4	2.3	19.5
92.8	25	127.6	8.6	70.3
120.6	0.2	0.3	-5.2	7.5
95.8	0.7	15	-10.1	9.3
174.2	125.7	74.7	2.8	138.2
161	2.9	50.5	2.3	25.5
304.9	0.4	22.3	1.9	17
56.2	0.2	0.2	-3.4	3.6
361.3	0.3	34.9	-1.1	22.7
37	0.4	61.4	1.9	22.5
116.9	35	131	21.2	87.4
43.5	0.3	1.7	0.2	14.4
534.9	1.3	93.6	-1.2	58.1
386.1	49.1	96.4	-15.4	104.8
253.1	4.9	44	2	34.5
184.7	0.7	15.4	0.8	11.3
168.3	2.6	130.5	1.4	34.9
120	1.1	239.4	0.8	17.8
1734	0.3	718.7	73.2	301.9
162.9	36.1	21.2	9.4	87.4
231.8	231.2	53	-64.3	310.6
788.2	360	77	36.1	1077.9
206.9	94.3	657.3	8	275
145.4	1.9	18.1	7.3	21.2
749.3	258	122.9	-58.2	468.7
76	1.3	11.2	-4.2	8.9
509.9	10.3	270.7	8.4	157.2
87.2	29.5	6.7	5.1	59.8
468.1	493.5	359.7	13.5	306.5
2682.8	96.8	207.2	14.3	231.1
166.7	49.4	27.3	11.6	124
244	3.6	54.9	5.5	57.6
173	16.5	17.5	-9.7	40.3
242.6	80.4	21.8	12.9	204.7
112.6	237.1	51.1	3.2	288.6
828.5	451.6	5006.4	33.4	1083.1
884.2	442.3	127.3	1.2	1619.2
151.5	267.1	81.3	18.1	455.7
436.8	0.3	42.7	3	55.7
67.6	0.1	83	4.1	44
82.6	0.2	80.2	3.8	56.9
616.4	0.3	118.2	10.9	142.2
242.7	0.3	62.2	11.8	1231.1
296.5	0.4	0.9	-6.9	36
1622.2	0.4	377.8	51.3	370.5
53.8	0.7	0.2	-6.1	3.9
374.2	0.8	21.2	-3.9	42.9
466.7	0.8	81	-17.2	103.5
359.7	0.9	171.2	-4.6	171.6
1132.6	1.5	75.6	19.5	136.4
891.9	2.5	253.4	11.2	128.8
338.2	2.7	63.8	-1.6	58.8
186.7	2.8	10.8	-6.1	48
68.7	2.8	4	1.4	52.8
605.8	3.3	41.6	9	92.6
942.8	6.7	147.8	11.7	192.8
366.5	7.6	119.3	22.7	157.5
334.8	9.5	20.2	0.9	302.8
1655.3	14.8	609.8	12.4	141.7
133.9	17.4	94.3	4.8	92.5
495.7	29.6	287.1	14.6	258.9
194.3	35.5	351.9	17.4	225.7
1516.7	41.8	1.1	0.6	579.2
856.4	55.9	135.1	8.7	210.4
458.3	100	293.8	23	192.6
2058.3	111.6	1085.8	-50.2	639.8
75.4	137	17.5	4.4	528.2
318.9	137.3	84.1	17.1	242.7
312.1	142.6	96.2	-6.5	235.3
681.8	178.9	387.7	33.7	416.8
760	180.7	1041.2	21.7	741.9
392.3	184.3	267.3	15.1	498.5
434.7	188.5	77.4	15	325.1
198	192	418.2	13.9	634.1
908.9	259.2	1330.9	48.9	985.5
998.2	269.6	94.8	14.5	323.5
670.6	340	1248.8	48.2	1211.5
949.9	349.4	138.9	102.4	848.6
1005.8	373.9	545.4	26.7	734.1
975.6	409.8	131.4	35	1045.6
38396.6	1112	4937	337	5469
730.6	1371.7	219.9	-1.9	584.5
5722.3	1577	4109	202	4134
1457.4	1836.4	869.1	96.7	3403.1
5397.3	1940.3	16121.5	299.7	5032.7
1486.9	2222	5905	342	4821
4024.7	3523	6804	259	9495
5449.9	4541	5465	449	11296
374	345.5	81.7	-21.7	233.1
2462.5	82.5	147.7	27.1	658.2
1048.3	3.5	4.9	-31.3	157.2
528.9	351.8	512.9	32.9	408.4
164.9	1.6	5.4	-6.9	37.6
694.7	397.7	154.8	35.4	534.8
333.8	116.1	233.3	12	251.7
312	155.2	45.9	14.4	397.4
2545.8	2004.5	2635.2	-432.3	6057
215.9	4.7	0.6	-12.6	26
473.5	3.4	106.3	18.4	88
1567.5	384.8	735.3	66.6	1154
741.6	23.3	671.4	11.3	303.7
240.4	1.8	22.4	7.2	27.4
325.4	7.1	188.9	-5.4	124
259.6	121.6	170.1	22.4	1873.8
486	74.7	102.5	43	911
874.9	207.3	499.4	73.1	3150
672.7	0.5	176.7	14.6	108.5
991.3	12.5	205.6	19.3	244.6
1039.5	1.5	101.7	7.5	74.3
306.5	24.5	346.3	24.5	320.5
56.3	1.5	245.9	2.1	82.4
182.5	6	8.9	0.4	26.2
830	310.4	982	39.1	767.9
484.8	236.6	231.8	8.3	188.3
76.2	1.8	84.9	6.1	44
409.7	6.4	25.2	-5	55.2
79.3	23.2	156.8	-5.7	127.5
501.8	86.3	432.5	9.5	206
176	9.5	664.1	7.9	155.1
1064.3	15.4	60.7	-32.6	147
215.3	68.8	300.2	-7.2	1132.8
1886.1	222.5	807.2	61.4	660
304.1	231.8	54.5	20.1	449.5
1335.6	1338.4	3494.3	74.4	3687.8
1571.7	0.7	11.4	-23	78.1
108.9	142.5	80.7	5.9	224.1
150.5	1.5	139.7	7.1	75.3
2390.7	146.8	1047.7	85.7	1276.5
165.2	262.5	39.8	8.2	378.5
452.4	1.3	8.8	-29.4	44.9
136.1	0.1	73.8	2.8	40.2
217.7	0.5	1.3	-18	47
252.9	1	94.8	3.9	39.4
78.1	2.6	0.9	-10.2	17.4
88.8	0.2	22.7	2.5	73.1
7415.8	554.4	763.3	142.7	1398.1
156.4	4.2	19.2	2	48.7
1318.8	24	510.6	48.7	1792.2
233.2	105.1	84.1	1	354.2
389.1	63.4	188.2	17	268
3201.6	466.2	317.8	25.1	595
312.9	38.3	119.7	4.9	181
1080	154.4	234.4	14.2	355.1
495	25.9	890	18.4	363.8
182.2	134.3	532.4	11.6	305.6
835.7	57.7	496.6	18.8	305.7
1626	82.7	399.6	24.8	360.8
609.4	8	183	10.8	196
988.2	335.9	201	24	447.3
482.5	2	2.7	-10.2	27.3
1111.2	375.4	353.4	12.6	755.6
927.6	42.1	336.5	21.6	173.6
52.3	0.9	5.1	-6.1	13.3
123	123.1	55.9	-16.7	178.7
567.8	315.3	133	-3.4	466
236.2	0.5	110	-32.7	72.7
266.7	26.5	37.4	17.6	225.1
763.1	243.2	388.2	38.5	295.8
188.3	7.8	328.7	8.9	152.9
790.4	344.4	442	26.6	1064.8
570.5	2384	565	-82	3557
1442.9	354.1	2732.1	101.1	1213.7
2418.3	0.4	51.7	-3.8	122.2
1072.7	118.5	949.8	78.7	7594.8
87.2	9.4	97.5	2.9	42.9
466	9.7	41.8	-11.5	100.3
608.5	16	350.9	20.3	254
308	1.8	104.9	7	40.6
953	116.5	3155	35.4	558.8
315.7	9.7	132.9	16.1	119.4
416	2295	130.6	9.6	137
276.7	241.4	157.9	-25.4	230.8
221.6	10.1	40.4	1.5	38.7
83.1	20.2	38.7	10.6	133.5
137.3	57.8	70.2	-8.4	139.5
167.7	210	83.1	11.4	277.2
277.7	163.7	1082.2	16.1	379.1
353.9	70	155.9	27.2	687.5
643.3	0.2	0.5	-11.7	11.3
171.9	0.5	22.5	2.2	31.5
305.6	42.4	21.8	4.9	173.4
926.2	7	137.3	23.3	204.6
559.2	346.2	87.9	16.7	737.6
43	0.1	16	1.9	14.6
448.1	79.8	79.5	32.8	842.6
968	27.7	641.1	53.3	1130.9
712.4	68.7	209.1	17	141.4
104.9	0.6	14.9	-1.4	6.8
288.3	125.2	128	9.9	216.1
323.6	144.9	161.7	1.5	418371
161.3	1.6	17.3	2.2	22.8
323.9	2	47.1	2.7	43.9
51.4	2.4	18.6	1.4	22.4
227.8	65.7	576.3	28.2	316.7
125.9	2.2	0.9	-5.2	15.5
120.6	0.1	32.8	1.3	26.5
1415.9	2.8	83.2	-2.1	64.4
456.8	0.7	57.1	3.6	108.4
324.1	282.8	729.4	17	824.2
289.8	0.4	58.5	3.5	23.2
759	139.9	21.3	1.7	73.6
218.4	1.2	11.8	0.4	11.7
100.1	6.9	143.9	7	36
77.3	41.2	130.4	4.2	100.3
356.4	1.2	1	-10.8	24.1
69.9	3.5	8.8	-12.9	29.1
139.8	0.8	36.2	5.8	32.8
307.2	22.6	41.4	4.6	90.8
2047.3	143.3	78.9	-57.1	260.3
53.2	7.2	22	0.6	16.5
656.3	250	924.6	28.1	1512.9
167.8	0.7	9.6	-3.3	10.6
1253.1	2.9	634.5	33.1	247.5
34.8	0.1	38.2	-0.6	18.1
20.7	20.1	59.6	1.3	16.4
76.4	0.8	19.9	-1.4	9.4
372.7	2	27.4	-22.7	57.3
73.7	1.2	78.2	-1.4	40.9
226	0.1	25.6	3.7	24
79.2	0.9	7.2	2	9.6
36.2	241.8	49.7	6.2	608.4
184.5	9.9	3.1	-20.7	43.8
333	5.9	819.4	6.6	259.6
67.3	1.2	10	-1.9	4.3
277.2	1.5	125.4	-1.5	48.9
388.2	219.9	210.5	-7.6	304.7
841.6	0.1	19.7	16.9	51.3
52.3	1.6	19.7	-4.4	22.4
176.4	1.1	3.8	-8.7	11.6
87.6	5.1	25.4	1.3	40.7
267.4	0.1	117.9	-16.4	65.1
21.7	0.8	5.8	-11.3	9.8
696.7	353.9	91.3	-20.1	125.9
638.4	125	415.6	7.1	347.6
146.5	3.7	211.8	8.4	88.7
103.6	0.7	25.3	1	12
37.1	2.1	4.6	-4	11
219.1	48.2	306.1	10.4	167.4
138.4	1.4	1.7	-5.8	22.3
257.9	0.7	69.7	-8.3	79.5
4341.6	46	508.1	20.1	341.4
140.8	5.1	26.3	4.1	35.9
136.2	13.5	1034.9	4.6	281.9
73.2	0.2	5.6	-5.7	4.7
219.2	2.5	31.6	4.7	59.6

Answer 1

1.)

data=read.csv(file.choose())# to read the given data.
y=data$ShareValue # response variable of regression.
x1=data$FirmDebt  
x2=data$TotalSales # x1,x2,x3,x4 are the corresponding regressor variable
x3=data$Net_Income
x4=data$TotalAssets
l=lm(y~x1+x2+x3+x4)
l

Output:

Call:
lm(formula = y ~ x1 + x2 + x3 + x4)

Coefficients:
(Intercept) x1 x2 x3 x4  
3.408e+02 1.608e-01 2.984e-01 1.552e+01 1.844e-04  

# the value of the coefficients are given in the above.

2.) and 3.)

summary(l)

Output:

> summary(l)

Call:
lm(formula = y ~ x1 + x2 + x3 + x4)

Residuals:
Min 1Q Median 3Q Max
-6282.1 -337.9 -219.5 30.3 31172.3

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 3.408e+02 1.221e+02 2.791 0.00558 **
x1 1.608e-01 3.277e-01 0.491 0.62409   
x2 2.984e-01 1.366e-01 2.184 0.02970 *  
x3 1.552e+01 2.698e+00 5.753 2.14e-08 ***
x4 1.844e-04 4.838e-03 0.038 0.96962   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2020 on 304 degrees of freedom
Multiple R-squared: 0.2548, Adjusted R-squared: 0.245
F-statistic: 25.99 on 4 and 304 DF, p-value: < 2.2e-16

## from the above table the if we observe the p-value , then it is clear that when we test the equality of regression coefficients with zero i,e H_o: b_i=0,(where b_i are the four regression coefficients ) then all the test is not significant. star marks(*, **, ***) are significant at level of significance 0.05. Hence, multicolinearity may present into the data set .

## On the other hand presence of multicolinearity can be tested by Condition number= where is the eigen value of the matrix () where is the data matrix . =(FirmDebt,TotalSales,Net_Income,TotalAssets). Multicolinearity present into the dataset if condition no>20.

r-code:

X=cbind(x1,x2,x3,x4)
eigen(t(X)%*%X)

output:

eigen() decomposition
$values
[1] 175539557562 539739405 37893909 559859

$vectors
[,1] [,2] [,3] [,4]
[1,] -1.290562e-03 -0.267242591 0.9633580959 -2.282347e-02
[2,] -2.433285e-03 -0.963218961 -0.2677453013 -2.271050e-02
[3,] -8.054405e-05 -0.027989111 0.0159148032 9.994815e-01
[4,] -9.999962e-01 0.002690944 -0.0005930566 4.213941e-06

### now highest eigenvalu=175539557562 and smallest eigen value= 559859

and condition no =559 which implies presence of multicolinearity.

5.)

Breusch-Pagan test: is given by the plot of residual of the reagression with y variable . If there is a pattern into the graph Heteroscadasticity present into the data set.

## Breusch-Pagan test##
r=resid(l)
plot(r,y)

6.)

a) from the first table we already see that p-value< 0.05.

output:

Residual standard error: 2020 on 304 degrees of freedom
Multiple R-squared: 0.2548, Adjusted R-squared: 0.245
F-statistic: 25.99 on 4 and 304 DF, p-value: < 2.2e-16.

#hence predictor is significant.

b) coefficints of x2=

2.984e-01

hence keeping all unit fixed increase 1 unit sales implies 2.984e-01 unit increse in share value. therefore 20 unit inrease in sale implies 20* 2.984e-01=23(approx).hence increasing sale implies increasing share value at least 5 unit is possible.