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PC World rated four component characteristics for 10 ultraportable laptop computers: features, performance, design, and price. Each characteristic was rated using a $0-100$ point scale. An overall rating, referred to as the $P C$ World Rating, was then developed for each laptop. The following table shows the features rating and the $P C$World Rating for the 10 laptop computers $(\mathrm{PC}$ World website, February $5,2009).$ $$\begin{array}{l}{\text { a. Develop a scatter diagram with the features rating as the independent variable. }} \\ {\text { b. What does the scatter diagram developed in part (a) indicate about the relationship }} \\ {\text { between the two variables? }}\end{array}$$ $$\begin{array}{l}{\text { c. Use the least squares method to develop the estimated regression equation. }} \\ {\text { d. Predict the } P C \text { World Rating for a new laptop computer that has a features rating }} \\ {\text { of } 70 .}\end{array}$$
According to the study of science and engineering indicators by the National Science Foundation (www.nsf.gov), the number of female graduate students in science and engineering disciplines has increased over the last 30 years. In $1981,24 \%$ of mathematics graduate students were female and $23 \%$ of graduate students in computer science were female. In $1991,32 \%$ of mathematics graduate students and $21 \%$ of computer science graduate students were female. In $2001,38 \%$ of mathematics graduate students and $30 \%$ of computer science graduate students were female. Write three $2 \times 1$ matrices representing the percentage of female graduate students. $$\begin{array}{l}A=\left[\begin{array}{l}\mathscr{F} \text { female-math }-1981 \\\mathbb{F} \text { female-C.S. }-1981\end{array}\right] \\B=\left[\begin{array}{l}\mathscr{F} \text { female-math }-1991 \\\mathscr{F} \text { female-C.S. }-1991\end{array}\right] \\C=\left[\begin{array}{l}\mathscr{F} \text { female-math }-2001 \\\mathscr{F} \text { female-C.S. }-2001\end{array}\right]\end{array}$$ What does $C-B$ tell us? What does $B-A$ tell us? What can you conclude about the number of women pursuing mathematics and computer science graduate degrees? Note: $\mathbf{C . S .}=$ computer science.
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PC World rated four component characteristics for 10 ultraportable laptop computers: features; performance; design; and price. Each characteristic was rated using a $0-100$ point scale. An overall rating, referred to as the $P C$ World Rating, was then devel oped for each laptop. The following table shows the performance rating, features rating, and the $P C$ World Rating for the 10 laptop computers (PC World website, February $5,$ $2009 ) .$ $\begin{array}{l}{\text { a. Determine the estimated regression equation that can be used to predict the } P C \text { World }} \\ {\text { Rating using the performance rating as the independent variable. }} \\ {\text { b. Determine the estimated regression equation that can be used to predict the } P C \text { World }} \\ {\text { Rating using both the performance rating and the features rating. }}\end{array}$$\begin{array}{l}{\text { c. Predict the } P C \text { World Rating for a laptop computer that has a performance rating of } 80} \\ {\text { and a features rating of } 70 .}\end{array}$
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