Question

 

Data set 2 presents a sample of the number of defective flash drives produced by a small manufacturing company over the last 30 weeks. Use Excel's Analysis ToolPak (or any statistical package that you are comfortable with) to compute the regression equation for predicting the number of defective flash drives over time (in weeks), the correlation coefficient r and the coefficient of determination R2. Submit your statistical output from Excel, which should include values for a slope, y-intercept, regression equation, r, and R2, and a one-page Word document in which you present an analysis of your results.

SUMMARY OUTPUT		Regression equation: $ Flashdrives: = 6.2989 + .0474 week
Regression Statistics			Intercept = 6.2989
Multiple R	0.30301		Slope = 0.0474
R Square	0.09181
Adjusted R Square	0.05938
Standard Error	1.33524
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5.046607341	5.046607341	2.830625754	0.103603045
Residual	28	49.92005933	1.782859262
Total	29	54.96666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6.29885	0.500010149	12.59744544	4.69443E-13	5.274626214	7.323074935	5.274626214	7.323074935
X Variable 1	0.04739	0.02816493	1.68244636	0.103603045	-0.01030726	0.105079229	-0.01030726	0.105079229

Answer 1

 

we have given ouput of the regression model :

here dependent varaible : Flashdrives

and independent variable : week

total observation is 30

## Estimated regression model :

$ Flashdrives = 6.2989 + ( 0.474 * week)

Here y intercept is = 6.2989

and slope = 0.474 ( it is positive)

interpretation for slope : from the regression model if x value increases as 1 week then flashdrives increases as 0.474 Flashdrives.

## Multiple R = 0.3030 ( it is also called correlation coefficient )

It is positive that is there is positive relationship between flashdrives and week but it is week ie (Multiple R < 0.5)

## R square = 0.09181  

it is coefficient of determination value = 0.09181

that is variation explained by model is = 9.181 % which is very less and weak .

## test for overall model :

To test : Ho : overall model is not significant vs H1 : overall model is significant .

test statistics = F = ( MS regression /MS error )  

= 5.0466073 / 1.782859262

= 2.8306257

p value = 0.103639  

Decision : we reject Ho if p value is less than alpha value using p value approach here p value is greater than alpha value here we fail to reject Ho .

Conclusion : there is Insufficient evidence to conclude that overall model is significant .

( that is overall model is not significant )

## test for intercept :

To test : Ho : intercept is significant ( β = 0 )

vs H1 : intercept is not significant . ( β  ≠ 0 )

Test statistics =

t = 12.59744544

p value = less than 0.00001

Decision : we reject Ho if p value is less than alpha value here p value is less than alpha value here we reject Ho .

Conclusion : Threre is sufficient evidence to conclude that y intercept is significant .

### Test for slope :

to test : Ho : slope is significant ( β1= 0 )

vs H1 : slope is not significant . ( β1 ≠ 0 )

test statistics =

t = 1.68244636

p value = 0.103639  

Decision : we reject Ho if p value is less than alpha value here p value is greater  than alpha value

here we fail to reject Ho .

Conclusion : Threre is Insufficient evidence to conclude that slope  is significant .

( that is slope is not significant )