Q$2.(45$ points$)$ Given below is data regarding Price & Quality ratings of different Treadmills in the market alongwith the Satisfaction Scores assigned by customers to each of the brands. Run a regression to determine if the Satisfaction Scores of the different brands is related to Price and Quality and answer the following questions. a$.$ Write the regression equation based on the output $($use the names of the variables$).$ b$.$ What does the R$-$square value represent? c$.$ Is Price a significant factor in overall customer satisfaction score at $95\%$ confidence level? d$.$ Is Quality a significant factor in overall customer satisafction score at $95\%$ confidence level? e$.$ Estimate the score of a treadmill whose Price is $$2500$ and which has a Very Good rating. Show your working. Brand & Model Price $($$$)$ Quality Score Landice L$72900$ Excellent $86$ NordicTrack S$30003500$ Very good $85$ SportsArt $31102900$ Excellent $82$ Precor $3500$ Excellent $81$ True Z$4$ HRC $2300$ Excellent $81$ Vision Fitness T$95002000$ Excellent $81$ Precor M $9\mathrm{.}313000$ Excellent $79$ Vision Fitness T$92001300$ Very good $78$ Star Trac TR$9013200$ Very good $72$ Trimline T$350$HR $1600$ Very good $72$ Schwinn $820$p $1300$ Very good $69$ Bowflex $7-$Series $1500$ Excellent $83$ NordicTrack S$19002600$ Very good $83$ Horizon Fitness PST$81600$ Very good $82$ Horizon Fitness $5\mathrm{.}2$T $1800$ Very good $80$ Evo by Smooth Fitness FX$301700$ Very good $75$ ProForm $1000$S $1600$ Very good $75$ Horizon Fitness CST$4\mathrm{.}51000$ Very good $74$ Keys Fitness $320$t $1200$ Very good $73$ Smooth Fitness $7\mathrm{.}1$HR Pro $1600$ Very good $73$ NordicTrack C$23001000$ Good $70$ Spirit Inspire $1400$ Very good $70$ ProForm $7501000$ Good $67$ Image $19\mathrm{.}0$ R $600$ Good $661$ Q$2.(45$ points$)$

$2$ Given below is data regarding Price $\backslash$& Quality ratings of different Treadmills in the market alongwith the Satisfaction Scores assigned by customers to each of the brands.

$3$ Run a regression to determine if the Satisfaction Scores of the different brands is related to Price and Quality and answer the following questions.

$4$ a$.$ Write the regression equation based on the output $($use the names of the variables$).$

$5$ lb$.$ What does the R $-$square value represent?

$6$ c$.$ Is Price a significant factor in overall customer satisfaction score at $\backslash (95\backslash \%\backslash )$ confidence level?

$7$ d$.$ Is Quality a significant factor in overall customer satisafction score at $\backslash (95\backslash \%\backslash )$ confidence level?

$8$ le$.$ Estimate the score of a treadmill whose Price is $\backslash (\backslash$$ $2500\backslash )$ and which has a Very Good rating. Show your working.

$10$ Brand $\backslash$& Model $\backslash (\backslash$quad $\backslash )$ Price $(\backslash$$$)$ Quality Score

$11|$andiceL$7$

$12$ NordicTrack S$3000$

$13$ SportsArt $3110$

$14$ Precor

$15$ True Z$4$ HRC

$16$ Vision Fitness T$9500$

$17$ Precor M $9\mathrm{.}31$

$18$ Vision Fitness T$9200$

$19$ Star Trac TR$901$

$20$ Trimline T$350$HR

$21$ Schwinn $820$p

$22$ Bowflex $7-$Series

$23$ NordicTrack S$1900$

$24$ Horizon Fitness PST$8$

$25$ Horizon Fitness $5\mathrm{.}2$T

$26$ Evo by Smooth Fitness FX$30$

$27$ ProForm $1000$S

$28$ Horizon Fitness CST$4\mathrm{.}5$

$29$ Keys Fitness $320$t

$30$ Smooth Fitness $7\mathrm{.}1$HR Pro

$31$ NordicTrack C$2300$

$32$ Spirit Inspire

$33$ ProForm $750$

$34$ Image $19\mathrm{.}0$R