Question

Find the ‘best fit’ equation of net income for last year on last year’s sales. Test the significance of the overall model at 1% level of significance.

Company	Market value	Sales	Profits	Assets	Recent share price	P-E Ratio	Yield
1	42926	9663	2446.6	11086	38	18	2.67
2	31557	37799	975.0	38870	47	33	3.76
3	19143	7230	1093.5	9590	59	18	2.85
4	9915	4908	737.6	19429	46	16	6.66
5	9094	989	267.7	1203	30	37	0.00
6	7206	13428	952.4	111896	70	8	1.72
7	7164	5814	319.4	5662	68	22	2.96
8	6340	3962	478.9	12578	29	15	4.87
9	4996	3525	183.1	3987	33	27	1.92
10	4211	3702	56.8	4070	33	74	3.30
11	4041	4102	282.3	50863	54	17	2.23
12	3789	1619	79.2	1490	87	48	0.32
13	3744	8311	194.0	5458	60	19	3.16
14	3618	3832	128.0	2769	35	20	0.00
15	3200	3434	190.0	7483	29	21	5.54
16	3167	2330	146.1	2458	58	22	2.43
17	2759	3472	138.6	3175	205	19	0.49
18	2636	1172	172.7	6455	27	15	3.31
19	2567	3858	91.4	3188	19	36	3.20
20	2416	6895	115.6	1812	21	22	0.00
21	2300	1553	202.3	4802	27	13	6.23
22	2206	1739	139.6	3005	33	16	0.61
23	2012	3376	65.2	2994	34	31	1.18
24	2010	1773	133.8	6859	18	24	0.00
25	1994	3389	28.0	3266	43	66	2.64
26	1707	644	29.4	845	41	58	0.98
27	1612	5550	120.7	3162	34	13	4.71
28	1404	505	107.1	2273	27	14	5.77
29	1318	2152	99.0	2008	28	14	2.12
30	1285	1220	64.7	920	13	20	1.85
31	1281	2867	112.6	15925	28	11	3.67
32	1261	577	60.5	628	34	21	0.00
33	1253	840	84.9	13626	38	21	0.74
34	1216	1386	102.6	16844	38	13	3.73
35	1066	2219	39.1	1662	21	27	1.76
36	1060	2650	53.7	1479	35	20	1.47
37	1034	219	10.6	250	30	57	0.00
38	1021	819	34.3	1566	37	28	0.00
39	1011	3352	54.4	1319	21	20	0.00
40	956	528	42.5	438	27	22	2.48
41	832	966	69.7	1844	38	9	2.86
42	824	461	55.4	502	24	15	0.00
43	805	883	16.1	495	35	47	0.00
44	788	600	39.7	584	31	22	0.65
45	692	389	26.6	497	30	25	0.00
46	633	708	35.8	1020	24	20	5.45
47	616	526	40.9	475	27	16	2.12
48	602	351	50.7	3916	48	12	3.60
49	585	453	27.1	331	44	23	0.63
50	581	705	39.4	472	20	15	3.16

Find the ‘best fit’ equation of net income for last year on last year’s sales. Test the significance of the overall model at 1% level of significance.

Answer 1

> # Reading the data in console > df = read.csv(file.choose(),header = T) > colnames(df) [1] "Company" "Market.value" "Sales" "Profits" [5] "Assets" "Recent.share.price" "P.E.Ratio" "Yield" > dim(df) [1] 50 8 > str(df) 'data.frame': 50 obs. of 8 variables: $ Company : int 1 2 3 4 5 6 7 8 9 10 ... $ Market.value : int 42926 31557 19143 9915 9094 7206 7164 6340 4996 4211 ... $ Sales : int 9663 37799 7230 4908 989 13428 5814 3962 3525 3702 ... $ Profits : num 2447 975 1094 738 268 ... $ Assets : int 11086 38870 9590 19429 1203 111896 5662 12578 3987 4070 ... $ Recent.share.price: int 38 47 59 46 30 70 68 29 33 33 ... $ P.E.Ratio : int 18 33 18 16 37 8 22 15 27 74 ... $ Yield : num 2.67 3.76 2.85 6.66 0 1.72 2.96 4.87 1.92 3.3 ... > summary(df) Company Market.value Sales Profits Assets Min. : 1.00 Min. : 581 Min. : 219.0 Min. : 10.60 Min. : 250 1st Qu.:13.25 1st Qu.: 1024 1st Qu.: 735.8 1st Qu.: 44.55 1st Qu.: 1066 Median :25.50 Median : 1850 Median : 1962.5 Median : 95.20 Median : 2882 Mean :25.50 Mean : 4209 Mean : 3468.9 Mean : 220.71 Mean : 7951 3rd Qu.:37.75 3rd Qu.: 3712 3rd Qu.: 3799.5 3rd Qu.: 180.50 3rd Qu.: 6257 Max. :50.00 Max. :42926 Max. :37799.0 Max. :2446.60 Max. :111896 Recent.share.price P.E.Ratio Yield Min. : 13.00 Min. : 8.00 Min. :0.000 1st Qu.: 27.00 1st Qu.:15.25 1st Qu.:0.520 Median : 33.50 Median :20.00 Median :2.120 Mean : 39.52 Mean :24.40 Mean :2.196 3rd Qu.: 42.50 3rd Qu.:26.50 3rd Qu.:3.275 Max. :205.00 Max. :74.00 Max. :6.660 > plot(df) > cor(df[,-1]) Market.value Sales Profits Assets Recent.share.price Market.value 1.00000000 0.6922622439 0.9341491 0.2761694 0.1110567665 Sales 0.69226224 1.0000000000 0.5452554 0.5097578 0.1532372418 Profits 0.93414905 0.5452554054 1.0000000 0.4174388 0.1232055395 Assets 0.27616939 0.5097577692 0.4174388 1.0000000 0.1870074786 Recent.share.price 0.11105677 0.1532372418 0.1232055 0.1870075 1.0000000000 P.E.Ratio -0.01095553 0.0004982515 -0.1736945 -0.2136470 -0.0004741459 Yield 0.17005089 0.1828134131 0.2154797 0.1271457 -0.1053225181 P.E.Ratio Yield Market.value -0.0109555282 0.1700509 Sales 0.0004982515 0.1828134 Profits -0.1736944984 0.2154797 Assets -0.2136469763 0.1271457 Recent.share.price -0.0004741459 -0.1053225 P.E.Ratio 1.0000000000 -0.2648121 Yield -0.2648120721 1.0000000 > # Here the net income is profit. > #Fitting the equation of net income for last year on last year’s sales > mod = lm(Profits~Sales, data = df) > summary(mod) Call: lm(formula = Profits ~ Sales, data = df) Residuals: Min 1Q Median 3Q Max -590.41 -98.62 -68.27 -22.69 1983.27 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 84.829673 57.131079 1.485 0.144 Sales 0.039170 0.008692 4.506 4.23e-05 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 343.1 on 48 degrees of freedom Multiple R-squared: 0.2973, Adjusted R-squared: 0.2827 F-statistic: 20.31 on 1 and 48 DF, p-value: 4.229e-05 # here p value is 4.229e-05 <0.01, so it is significant at 1% level > #Fitting the equation of net income for last year on last year complete data > df1 = df[,-1] # since company number is unique for each data point therefore it has no importance > mod1 = lm(Profits~ .,df1) > summary(mod1) Call: lm(formula = Profits ~ ., data = df1) Residuals: Min 1Q Median 3Q Max -211.494 -25.299 -2.766 32.283 142.073 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 56.3927458 32.4206991 1.739 0.0891 . Market.value 0.0587314 0.0019425 30.234 < 2e-16 *** Sales -0.0262996 0.0029623 -8.878 2.81e-11 *** Assets 0.0062518 0.0007296 8.568 7.55e-11 *** Recent.share.price 0.1368850 0.3895267 0.351 0.7270 P.E.Ratio -2.6194392 0.7825693 -3.347 0.0017 ** Yield 7.8043555 6.0061320 1.299 0.2007 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 73.92 on 43 degrees of freedom Multiple R-squared: 0.9708, Adjusted R-squared: 0.9667 F-statistic: 238.2 on 6 and 43 DF, p-value: < 2.2e-16 # Here we see that Market.value, sales and assets have significant effect at 1% level.

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