Defective Flash Drives: Correlation and Regression Analysis

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Methodology

The data of the number of defective flash drives manufactured by a small manufacturing company was obtained by counting them weekly for 30 weeks and then recorded against each week as presented in the Excel file. The Analysis Toolpak of MS Excel in performing correlation and regression analyses. According to Black (2009), correlation and regression analyses require variables to be on a continuous scale. The correlation coefficient (r) was used in interpreting the strength and the nature of the relationship between time and defective flash drives while R-square (R²) was used in predicting the influence of time on the number of defective flash drives. Moreover, the regression equation was formulated using the y-intercept and correlation coefficient.

Analysis

The correlation table indicates that there is a moderate relationship between time (week) and the number of defective flash drives, r = 0.303.

Table 1: Correlation.

	Week	#Defective Flash Drives
Week	1
#Defective Flash Drives	0.303	1

The regression analysis shows that time (week) explains 9.2% of the variation in the number of defective flash drives (R²= 0.092).

Table 2: Regression.

Multiple R	0.303
R Square	0.092
Adjusted R Square	0.059
Standard Error	1.335
Observations	30

Sharma (2012) asserts that the ANOVA table determines if a regression model is statistically significant or not in predicting the relationship between variables. The ANOVA table reveals that the regression model is not statistically significant in predicting the influence of time (week) on the number of defective flash drives, F(1,28) = 2.831, p = 0.104.

Table 3: ANOVA.

	df	SS	MS	F	*Significance F*
Regression	1	5.047	5.047	2.831	0.104
Residual	28	49.920	1.783
Total	29	54.967

The table of coefficients (Table 4) shows that the y-intercept is 6.299 and the gradient of time is 0.047, which forms the regression equation. In this view, the regression equation is that the number of defective flash drives = 0.047(week) + 6.299. The gradient indicates that a unit change in the dependent variable results in a change of the dependent variable by the gradient coefficient (Sharpe, De Veaux, & Velleman, 2015). Therefore, the regression equation implies that an increase in time by a week results in an increase in the number of defective flash drives by 0.047.

Table 4: Coefficients.

	*Coefficients*	*Standard Error*	*t Stat*	*P-value*	*Lower 95%*	*Upper 95%*
Intercept	6.299	0.500	12.597	0.000	5.275	7.323
Week	0.047	0.028	1.682	0.104	-0.010	0.105

References

Black, K. (2009). Business Statistics: Contemporary Decision Making. New York: John Wiley & Sons.

Sharma, J. K. (2012). Business statistics. New Delhi: Dorling Kindersley.

Sharpe, N., De Veaux, R., & Velleman, P. (2015). Business Statistics. New York: Pearson Education.