Question $23$

$4$ pts

We record the amount of time $(x$ in minutes$)$ per day a group of $12$ high school girls spend using their cell phone $($texting$,$ talking, and Web use$).$ We also record the overall GPA $($y$)$ of each girl.

Consider a linear regression model: GPA$={}_0+{}_1**$ Celltime

Below is a regression summary from the data:

GPA$=4\mathrm{.}01-0\mathrm{.}0153$ Cellitime

Predictor Coef $SE$ Coef $TP$

Constant $4\mathrm{.}0084,0\mathrm{.}2486,16\mathrm{.}12,0\mathrm{.}000$

Cellime $-0\mathrm{.}015334,0\mathrm{.}003226,-4\mathrm{.}75,0\mathrm{.}001$

Cellime $-0\mathrm{.}015334,0\mathrm{.}003226,-4\mathrm{.}75,0\mathrm{.}001$

$S=0\mathrm{.}472864,R-Sq=69\mathrm{.}38,R-Sq(adj)=66\mathrm{.}38$

Analysis of Variance

Source $DFSSMSFP$

Regression $1,5\mathrm{.}0519,5\mathrm{.}0519,22\mathrm{.}59,0\mathrm{.}001$

Residual Error $10,2\mathrm{.}2360,0\mathrm{.}2236,$

Total $11,7\mathrm{.}2879,$

Does there appear to be a significant linear relationship between the amount of cell phone use and GPA? $($use $=0\mathrm{.}01)$

yes, because the $p-$value from the test for significance is $0\mathrm{.}000.$

yes, because the $p-$value from the test for significance is $0\mathrm{.}001.$

no$,$ because the $R-$square value is too low.

yes, because the regression equation is defined.