A firm that prints automobile bumper stickers conducts a study to investigate th

Question

A firm that prints automobile bumper stickers conducts a study to investigate the relation between the direct cost of producing an order of bumper stickers and the number of stickers (thousands of stickers) in a particular order. Use SPSS and PROB6.sav. a. Is there reason to believe there is a linear relationship between RunSize and TOTCOST? Find the correlation between RunSize and TOTCOST. Is this linear correlation coefficient statistically significant and alpha = 01? b. Are there any outliers? Are there any influential points? Explain your answers. c. If appropriate, provide a predictive equation for predicting TOTCOST from RunSize. Write the predictive equation down. d. Show how the hypothesis for H_0: beta_1 = 0 is found in the SPSS output. Locate the p-value for this test. Is the p-value one-tailed or two-tailed?

Explanation / Answer

Here Runsize is independent variable and totalcost is dependent variable.

Here we have to fit regression of totalcoston Runsize.

I don't have SPSS so I can use EXCEL.

This we can find in EXCEL.

Steps :

ENTER data into EXCEL sheet --> Data --> Data Analysis --> Regression --> ok --> Input Y Range : select total cost range --> InputX Range : select Runsize range --> click on labels --> Output Range : select one empty cell --> ok --> ok

Here the regression equation is,

total cost = 99.8 + 51.9 runsize

R-sq = 99.6%

Interpreation : It expresses the proportion of variation in total cost which is explained by variation in run size.

We can test here overall significance and individual significance.

The hypothesis for both the significances are same.

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for runsize.

Or

H0 : There is no relationship between total cost and runsize.

H1 : There is relationship between total cost and runsize.

Assume alpha = level of significance = 0.05

We see that P-value for both the significance is 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : We get significant result about F test and t test.

The population slope for runsize is differ than 0.

There is some relationship between total cost and runsize.

By using regression equation we can predicttotal cost for given values of runsize

SUMMARY OUTPUT Regression Statistics Multiple R 0.998218433 R Square 0.996440041 Adjusted R Square 0.996312899 Standard Error 12.20653142 Observations 30 ANOVA df SS MS F Significance F Regression 1 1167746.817 1167747 7837.258 7.86E-36 Residual 28 4171.983461 148.9994 Total 29 1171918.8 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 99.77702511 2.827296992 35.29061 9.32E-25 93.98557 105.5685 93.98557 105.5685 runsize 51.9178567 0.586454986 88.52829 7.86E-36 50.71656 53.11916 50.71656 53.11916

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