Instruction 12 $\text { Regression statistics }$ $\text { ANOVA }$

question 29

Multiple Choice

Instruction 12.35
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:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.8691 \\\hline \text { R Square } & 0.7554 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7467 \\\hline \text { Standard Error } & 44.4765 \\\hline \text { Observations } & 30.0000\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\\hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\\hline \text { Total } & 29 & 226451.3503 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}$



-Referring to Instruction 12.35,which of the following is the correct alternative hypothesis for testing whether there is a linear relationship between revenue and number of downloads?

• A) H₁: b₁ = 0
• B) H₁: \(\beta\)₁ \(\neq\)0
• C) H₁: b₁ \(\neq\) 0
• D) H₁: \(\beta\)₁ = 0

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Definitions:

Variance

A statistical measure that represents the degree to which a set of numbers are spread out, calculated as the average of the squared differences from the Mean.

Sample Size

The number of observations or units that make up a statistical sample.

Genet

Edmond-Charles Genêt, a French diplomat who caused a controversy in 1793 by violating diplomatic protocol in the United States during the French Revolutionary Wars.

Neutrality Pact

An agreement between states to remain neutral, especially in a conflict, neither supporting nor opposing any side involved.