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SCENARIO 12-11
a Computer Software Developer Would Like to Use

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SCENARIO 12-11
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.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 sharewares that he has developed:
 SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.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 sharewares that he has developed:     \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\  \text { R Square } & 0.7554 \\  \text { Adjusted R Square } & 0.7467 \\  \text { Standard Error } & 44.4765 \\  \text { Observations } & 30.0000 \\ \hline \end{array}   ANOVA  \begin{array}{llll}  \hline & {\text { df }} & {\text { SS }} &{\text { MS }} & F & \text { Significance F } \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\  \text { Residual } & 28 & 55386.4309 & 1978.1582 & & \\  \text { Total } & 29 & 226451.3503 & & & \end{array}    \begin{array}{lllll} \hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\ \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\ \hline \end{array}    Simple Linear Regression 12-41   -Referring to Scenario 12-11, which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads? a)  H _ { 0 } : b _ { 1 } = 0  b)  H _ { 0 } : b _ { 1 } \neq 0  c)  H _ { 0 } : \beta _ { 1 } = 0  d)  H _ { 0 } : \beta _ { 1 } \neq 0  Regression Statistics  Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 Standard Error 44.4765 Observations 30.0000\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.8691 \\ \text { R Square } & 0.7554 \\ \text { Adjusted R Square } & 0.7467 \\ \text { Standard Error } & 44.4765 \\ \text { Observations } & 30.0000 \\\hline\end{array}

ANOVA
 df  SS  MS F Significance F  Regression 1171062.9193171062.919386.47590.0000 Residual 2855386.43091978.1582 Total 29226451.3503\begin{array}{llll} \hline & {\text { df }} & {\text { SS }} &{\text { MS }} & F & \text { Significance F } \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\ \text { Residual } & 28 & 55386.4309 & 1978.1582 & & \\ \text { Total } & 29 & 226451.3503 & & &\end{array}

 Coefficients  Standard Error  t Stat  P-value  Lower 95%  Upper 95%  Intercept 95.061426.91833.53150.0015150.200939.9218 Download 3.72970.40119.29920.00002.90824.5513\begin{array}{lllll}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}
 SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.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 sharewares that he has developed:     \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\  \text { R Square } & 0.7554 \\  \text { Adjusted R Square } & 0.7467 \\  \text { Standard Error } & 44.4765 \\  \text { Observations } & 30.0000 \\ \hline \end{array}   ANOVA  \begin{array}{llll}  \hline & {\text { df }} & {\text { SS }} &{\text { MS }} & F & \text { Significance F } \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\  \text { Residual } & 28 & 55386.4309 & 1978.1582 & & \\  \text { Total } & 29 & 226451.3503 & & & \end{array}    \begin{array}{lllll} \hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\ \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\ \hline \end{array}    Simple Linear Regression 12-41   -Referring to Scenario 12-11, which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads? a)  H _ { 0 } : b _ { 1 } = 0  b)  H _ { 0 } : b _ { 1 } \neq 0  c)  H _ { 0 } : \beta _ { 1 } = 0  d)  H _ { 0 } : \beta _ { 1 } \neq 0 Simple Linear Regression 12-41  SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware.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 sharewares that he has developed:     \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.8691 \\  \text { R Square } & 0.7554 \\  \text { Adjusted R Square } & 0.7467 \\  \text { Standard Error } & 44.4765 \\  \text { Observations } & 30.0000 \\ \hline \end{array}   ANOVA  \begin{array}{llll}  \hline & {\text { df }} & {\text { SS }} &{\text { MS }} & F & \text { Significance F } \\ \hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\  \text { Residual } & 28 & 55386.4309 & 1978.1582 & & \\  \text { Total } & 29 & 226451.3503 & & & \end{array}    \begin{array}{lllll} \hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\ \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\ \hline \end{array}    Simple Linear Regression 12-41   -Referring to Scenario 12-11, which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads? a)  H _ { 0 } : b _ { 1 } = 0  b)  H _ { 0 } : b _ { 1 } \neq 0  c)  H _ { 0 } : \beta _ { 1 } = 0  d)  H _ { 0 } : \beta _ { 1 } \neq 0
-Referring to Scenario 12-11, which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads? a) H0:b1=0H _ { 0 } : b _ { 1 } = 0
b) H0:b10H _ { 0 } : b _ { 1 } \neq 0
c) H0:β1=0H _ { 0 } : \beta _ { 1 } = 0
d) H0:β10H _ { 0 } : \beta _ { 1 } \neq 0


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