Homework #$7$

Due Apr $8$ via Canvas

$(10$ pts$.)$

Let$$s consider a similar problem where we actually keep up with the bed$-$time and the arrival time simultaneously. Both of these variables are continuous, so you should use regression to try and show if there is a relationship between the two variables. Use the data below to create a regression equation.

Bed Time

Arrival Time

Bed Time

Arrival Time

Bed Time

Arrival Time

$558$

$436$

$598$

$442$

$584$

$455$

$595$

$445$

$581$

$457$

$617$

$456$

$623$

$470$

$611$

$457$

$578$

$429$

$627$

$433$

$608$

$452$

$609$

$468$

$562$

$453$

$544$

$437$

$541$

$438$

$541$

$432$

$591$

$444$

$610$

$461$

$575$

$449$

$577$

$440$

$652$

$459$

$652$

$448$

$551$

$439$

$546$

$440$

$588$

$460$

$555$

$440$

$593$

$464$

$651$

$451$

$615$

$459$

$544$

$437$

$558$

$432$

$585$

$440$

$635$

$441$

$587$

$445$

$658$

$466$

$615$

$447$

$610$

$434$

$606$

$453$

$552$

$446$

$646$

$458$

$636$

$453$

$649$

$460$

$654$

$448$

$578$

$465$

$648$

$462$

$620$

$454$

$588$

$425$

$624$

$452$

$585$

$460$

$626$

$450$

The regression equation is

Arrival Time $=352\mathrm{.}8+0\mathrm{.}1605$ Bed Time

Model Summary

S

R$-$sq

R$-$sq$($adj$)$

$9\mathrm{.}71470$

$25\mathrm{.}23\%$

$23\mathrm{.}67\%$

Analysis of Variance

Source

DF

SS

MS

F

P

Regression

$1$

$1528\mathrm{.}70$

$1528\mathrm{.}70$

$16\mathrm{.}20$

$0\mathrm{.}000$

Error

$48$

$4530\mathrm{.}02$

$94\mathrm{.}38$

Total

$49$

$6058\mathrm{.}72$

A$)$ Interpret the coefficients of the equation.

B$)$ Interpret the R$-$square value.

C$)$ Do the results indicate that going to bed late has an influence on the arrival time? Explain your answer.

D$)$ Do these results support the decision that you made in the hypothesis test in Homework $6,$ Problem $3?$