Analysis of R&D Expenses and Assets in Firms

Business Statistics
1

Q1.R& D Expenses
Q2.
a. Scatter plot R&D Expense on Assets given underneath.
Figure 1: Scatter plot R&D Expense on Assets
The trend line in the two-way scatter plot revealed the positive linear and highly correlated
association between the two variables. From the coefficient of Determination of 0.952, it
was possible to explain 95.2% variation in R&D expenses by total assets of the firms.
Outliers were identified from the three sigma limits, and were clearly evident from the
scatter plot diagram. The companies with R&D expenses outside the three sigma range (-
1257.37, 1434.19) and assets outside (-14139.15, 16082.25) were identified as outlier
companies. But, presence of some outlier values of asset and expense were within the
confidence interval of the linear trend line. The scatter plot was redrawn by excluding the
outliers, and has been presented in Figure 2. Removal of outlier reduced the coefficient of
determination, and consequently diminished the predictability influence of the independent
factor.
2

Figure 2: Scatter plot R&D Expense on Assets – Without outliers
b. The least square regression line was estimated as R∧D Expense =0 .087∗Asset +3 .982 .
The intercept of 3.982 signified that R&D expenses were $ 3,982,000 for zero asset of the
company. Practically, the implication was statistically irrelevant (t = 0.883, p = 0.378)
and indicated that companies were investing aggressively on R&D purposes. The slope of
the regression of 0.087 was statistically significant (t = 98.778, p < 0.05) at 5% level of
significance, and implied a strong positive linear association between the variables.
Table 1: Regression Model for R&D on Assets
Regression Statistics
Multiple R 0.976
R Square 0.952
Adjusted R Square 0.952
Standard Error 98.292
Observations 493
ANOVA
df SS MS F Significance F
Regression 1 94265529.619 94265529.619 9757.100 0.000
Residual 491 4743661.117 9661.224
Total 492 99009190.736
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 3.982 4.509 0.883 0.378 -4.877 12.840
Assets 0.087 0.001 98.778 0.000 0.085 0.089
3

c. Coefficient of determination was 0.952, implying 95.2% variation in R&D expenses were
explained by total assets of the company. In fact, the adjusted R square for the inclusion of
Assets as an impact factor implied the statistical significance of the predictor (t = 98.78, p <
0.05). The standard error of 0.001 or 0.1% signified that the observations were within the
0.1% spread ($ -166940.16, $ 173716.20) of the regression equation. The regression line
accurately characterized the strong positive correlation between the variables.
d. The histograms of both the variables were highly right skewed, indicating presence of high
R&D expense, asset values for the companies. The scatter plot also indicated the same trend
of the data, and here also the similar trend was observed.
Figure 3: Histogram of Expense on R&D
Figure 4: Histogram of Assets
4