# Alex puts his spare change in a jar every night. if he has \$11.09 at the end of january \$22.27 at  the end of febuary \$44.35 in april \$75.82 in july \$ 89 in august and \$114.76 at the end of...

Alex puts his spare change in a jar every night. if he has \$11.09 at the end of january \$22.27 at  the end of febuary \$44.35 in april \$75.82 in july \$ 89 in august and \$114.76 at the end of october perfrom a linear regression on this data to complete the following items? alex wants to buy a video game at the end of december for \$140 will he have enough for this purchase? can you show me the calculations also please!

Asked on by quddoos

aruv | High School Teacher | (Level 2) Valedictorian

Posted on

We following points

(1,11.09),(2,22.27),(4,44.35),(7,75.82),(8,89.00),(10,114.76).

1   January

2   February

4    April

7    July

10   October

Let regression line be

`y=ax+b`  ,where a and b  are constants to be determined.

`xy=ax^2+bx`

Thus to determine a and b ,we have two equations as follows

`sumy=sum(ax)+sum(b)`

`sum(xy)=sum(ax^2)+sum(bx)`

`sumx=32`

`sumy=357.29`

`sumx^2=234`

`sum xy=2663.37`

Thus

357.29=32a+6b

2663.37=234a+32b

solving above system of equation

a=11.97

b=-4.29

So regression line is

`y=11.97x-4.29`

Alex wants to buy a video game at the end of December i.e x=12

`y=11.97xx12-4.29`

`y=139.35`

But video game available for \$140.But Alex has only \$139.35.So he has not enough money to buy video game.

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