Question

Before purchasing video conferencing equipment, a company run tests of its current internal computer network. The goal of the test was to measure how rapidly data moved through the network given the current demand on the network. Eighty files ranging in size from 20 to 100 megabytes (MB) were transmitted over the network at various time of the day, and the Transfer time (Sec) to send the files was recorded. Below are the regression results of these data.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.790286
R Square	0.624552
Adjusted R Square	0.619738
Standard Error	6.243347
Observations	80
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	7.274663	1.714906	4.242018	6.04E-05	3.860547	10.68878	3.860547	10.68878
File Size (MB)	0.313307	0.027505	11.39086	2.89E-18	0.258549	0.368066	0.258549	0.368066

1) What are the necessary conditions to be stratified for simple regression and inference statistics?

2) Based on the table on question, formulate the linear regression model and interpret the slope and Y-intercept

3) Based on the table on question, what is the standard error of the residual? Interpret this residual.

4) Based on the table on question, write the null and the alternate hypothesis for the slope and give the meaning of your hypothesis; undertake the hypothesis test for the slope by giving appropriate test statistics, p-value and conclusion in terms

Answer 1

1.

The necessary conditions to be stratified for simple regression and inference statistics:

A. The dependent variable Y has a roughly linear relationship with the independent variable X.

B. The residuals or errors should be independently follow Normal distribution with mean=0 and constant variance.

2.

Linear regression model:

Y=7.274663+0.313307x

where, Y=predicted value of y, y=Transfer time (Sec), x=File size (MB)

If file size is increased by 1 MB, then the expected transfer time is increased by 0.313307 sec.

Here Y-intercept has no physical interpretation.

3. Standard error of residual=6.243347 is the standard deviation of the difference between a set of observed and predicted values of transfer time and it seems that value of standard error of residual is small so we can conclude that fitting is good.

4.

i.e. we want to test the slope is different from zero or not or more specifically the regression equation is significant.

test statistic=t=11.39086

p-value=2.89x 10^-18

Since p-value<0.05 so we reject null hypothesis at 5% level of significance and conclude that the slope is significantly different from zero.