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!

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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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