A study has recently been conducted by a major computer magazine publisher in wh

Question

A study has recently been conducted by a major computer magazine publisher in which the objective was to develop a multiple regression model to explain the variation in price of personal computers. Three independent variables were used. The following computer printout shows the final output. However, several values are omitted from the printout.

Given this information, the regression model explains just under 70 percent of the variation in the price of personal computers.

SUMMARY OUTPUT Recression Statistics 0.834308875 Multiple R R Square Adjusted R Square Standard Error Observations ANOVA dif MS nificance F 2.07E-08 Regression Residual Total 3 34335282.67 14991966.89 35 49327249.56 Intercept Processor Mz RAM Hard Drive Capacit Coefficients Standard Error t Stat P-value Lower 95 %Upper 95% -45.95413592 730.8679496 0.06288 0.9502561534.68 1442.774 0.193481924 2.557161186 4.5215836542.94317936 174.042249 44.08895333

Explanation / Answer

The table still works like all ANOVA tables. A variance is a variation divided by degrees of freedom, that is MS = SS / df. The F test statistic is the ratio of two sample variances with the denominator always being the error variance. So F = MS(Regression) / MS(Residual).

R2 = ( SS(Total) - SS(Residual) ) / SS(Total).

R2 = (49327249.56 - 14991966.89)/49327249.56 = 0.6961 or 69.61%

So, hjust under 70%. Thus, statement is true.

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