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TABLE 13- 11
a Company That Has the Distribution Rights

Question 155

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TABLE 13- 11
A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles:
 Regression Statistics  Multiple R 0.8531 RSquare 0.7278 Adjusted R Square 0.7180 Standard Error 47.8668 Observations 30\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.8531 \\\text { RSquare } & 0.7278 \\\text { Adjusted R Square } & 0.7180 \\\text { Standard Error } & 47.8668 \\\text { Observations } & 30\end{array}\end{array}
ANOVA
 d f SS  MS F Significance FRegression 1171499.78171499.7874.85052.1259E−09Residual2864154.422291.23Total29235654.20\begin{array}{lrrrrr}\hline &\text { d f}& \text { SS } & \text { MS } & \text {F }& \text {Significance F} \\\hline \text {Regression }& 1 & 171499.78 & 171499.78 & 74.8505 & 2.1259E-09 \\\text {Residual} & 28 & 64154.42 & 2291.23 & & \\\text {Total} & 29 & 235654.20 & & & \\\hline\end{array}

Coefficients  Standard Error t Stat  p -value Lower 95% Upper 95%  Intercept 76.535111.83186.46865.24E−0752.2987100.7716Gross4.33310.50088.65162.13E−093.30725.3590\begin{array}{lrrrrrr}\hline & \text {Coefficients }& \text { Standard Error}& \text { t Stat }& \text { p -value }& \text {Lower 95\% }& \text {Upper 95\% }\\\hline \text { Intercept }& 76.5351 & 11.8318 & 6.4686 & 5.24 \mathrm{E}-07& 52.2987 & 100.7716 \\ \text {Gross} & 4.3331 & 0.5008 & 8.6516 & 2.13 \mathrm{E}-09 & 3.3072 & 5.3590 \\\hline\end{array}

TABLE 13- 11 A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles: \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l c } \hline \text { Multiple R } & 0.8531 \\ \text { RSquare } & 0.7278 \\ \text { Adjusted R Square } & 0.7180 \\ \text { Standard Error } & 47.8668 \\ \text { Observations } & 30 \end{array} \end{array} ANOVA \begin{array}{lrrrrr} \hline &\text { d f}& \text { SS } & \text { MS } & \text {F }& \text {Significance F} \\ \hline \text {Regression }& 1 & 171499.78 & 171499.78 & 74.8505 & 2.1259E-09 \\ \text {Residual} & 28 & 64154.42 & 2291.23 & & \\ \text {Total} & 29 & 235654.20 & & & \\ \hline\end{array} \begin{array}{lrrrrrr} \hline & \text {Coefficients }& \text { Standard Error}& \text { t Stat }& \text { p -value }& \text {Lower 95\% }& \text {Upper 95\% }\\ \hline \text { Intercept }& 76.5351 & 11.8318 & 6.4686 & 5.24 \mathrm{E}-07& 52.2987 & 100.7716 \\ \text {Gross} & 4.3331 & 0.5008 & 8.6516 & 2.13 \mathrm{E}-09 & 3.3072 & 5.3590 \\ \hline \end{array} TABLE 13-5 \begin{array}{lc} \hline \text {Regression Statistics } \\ \hline \text { Multiple R} & 0.802 \\ \text {R Square} & 0.643 \\ \text {Adjusted R Square} & 0.618 \\ \text {Standard Error SYX }& 0.9224 \\ \text {Observations} & 16 \\ \hline \end{array} ANOVA \begin{array}{lrlrlr} \hline & \text {d f } & \text { SS} & \text { MS } & \text {F } & \text { Sig.F }\\ \hline \text { Regression }& 1 & 21.497 & 21.497 & 25.27 & 0.000 \\ \text {Error }& 14 & 11.912 & 0.851 & & \\ \text {Total }& 15 & 33.409 & & & \\ \hline \end{array} \begin{array}{lllrr} \hline \text {Predictor} & \text {Coefficients} &\text { Standard Error }&\text { t Stat }& \text { p -value} \\ \hline \text {Intercept} & 3.962 & 1.440 & 2.75 & 0.016 \\ \text {Industry} & 0.040451 & 0.008048 & 5.03 & 0.000 \\ \hline \end{array} -Referring to Table 13-11, the null hypothesis that there is no linear relationship between box office gross and home video unit sales should be reject at a 5% level of significance. TABLE 13- 11 A company that has the distribution rights to home video sales of previously released movies would like to use the box office gross (in millions of dollars) to estimate the number of units (in thousands of units) that it can expect to sell. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different movie titles: \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l c } \hline \text { Multiple R } & 0.8531 \\ \text { RSquare } & 0.7278 \\ \text { Adjusted R Square } & 0.7180 \\ \text { Standard Error } & 47.8668 \\ \text { Observations } & 30 \end{array} \end{array} ANOVA \begin{array}{lrrrrr} \hline &\text { d f}& \text { SS } & \text { MS } & \text {F }& \text {Significance F} \\ \hline \text {Regression }& 1 & 171499.78 & 171499.78 & 74.8505 & 2.1259E-09 \\ \text {Residual} & 28 & 64154.42 & 2291.23 & & \\ \text {Total} & 29 & 235654.20 & & & \\ \hline\end{array} \begin{array}{lrrrrrr} \hline & \text {Coefficients }& \text { Standard Error}& \text { t Stat }& \text { p -value }& \text {Lower 95\% }& \text {Upper 95\% }\\ \hline \text { Intercept }& 76.5351 & 11.8318 & 6.4686 & 5.24 \mathrm{E}-07& 52.2987 & 100.7716 \\ \text {Gross} & 4.3331 & 0.5008 & 8.6516 & 2.13 \mathrm{E}-09 & 3.3072 & 5.3590 \\ \hline \end{array} TABLE 13-5 \begin{array}{lc} \hline \text {Regression Statistics } \\ \hline \text { Multiple R} & 0.802 \\ \text {R Square} & 0.643 \\ \text {Adjusted R Square} & 0.618 \\ \text {Standard Error SYX }& 0.9224 \\ \text {Observations} & 16 \\ \hline \end{array} ANOVA \begin{array}{lrlrlr} \hline & \text {d f } & \text { SS} & \text { MS } & \text {F } & \text { Sig.F }\\ \hline \text { Regression }& 1 & 21.497 & 21.497 & 25.27 & 0.000 \\ \text {Error }& 14 & 11.912 & 0.851 & & \\ \text {Total }& 15 & 33.409 & & & \\ \hline \end{array} \begin{array}{lllrr} \hline \text {Predictor} & \text {Coefficients} &\text { Standard Error }&\text { t Stat }& \text { p -value} \\ \hline \text {Intercept} & 3.962 & 1.440 & 2.75 & 0.016 \\ \text {Industry} & 0.040451 & 0.008048 & 5.03 & 0.000 \\ \hline \end{array} -Referring to Table 13-11, the null hypothesis that there is no linear relationship between box office gross and home video unit sales should be reject at a 5% level of significance.

TABLE 13-5
Regression Statistics  Multiple R0.802R Square0.643Adjusted R Square0.618Standard Error SYX 0.9224Observations16\begin{array}{lc}\hline \text {Regression Statistics } \\\hline \text { Multiple R} & 0.802 \\ \text {R Square} & 0.643 \\ \text {Adjusted R Square} & 0.618 \\ \text {Standard Error SYX }& 0.9224 \\ \text {Observations} & 16 \\\hline\end{array}

ANOVA
d f  SS MS F  Sig.F  Regression 121.49721.49725.270.000Error 1411.9120.851Total 1533.409\begin{array}{lrlrlr}\hline & \text {d f } & \text { SS} & \text { MS } & \text {F } & \text { Sig.F }\\\hline \text { Regression }& 1 & 21.497 & 21.497 & 25.27 & 0.000 \\ \text {Error }& 14 & 11.912 & 0.851 & & \\ \text {Total }& 15 & 33.409 & & & \\\hline\end{array}

PredictorCoefficients Standard Error  t Stat  p -valueIntercept3.9621.4402.750.016Industry0.0404510.0080485.030.000\begin{array}{lllrr}\hline \text {Predictor} & \text {Coefficients} &\text { Standard Error }&\text { t Stat }& \text { p -value} \\\hline \text {Intercept} & 3.962 & 1.440 & 2.75 & 0.016 \\\text {Industry} & 0.040451 & 0.008048 & 5.03 & 0.000 \\\hline\end{array}
-Referring to Table 13-11, the null hypothesis that there is no linear relationship between box office gross and home video unit sales should be reject at a 5% level of significance.

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