Question

Time $t$ (years)	$0$	$1$	$2$	$5$
Value $v\left(t\right)$ (dollars)	$15,000$	$13,000$	$10,900$	$3,000$

The present cost of a car is 15,000$.Itsvaluedepreciatesattherateshowninthetableabove.Basedonaleast-squareslinearregression,whatisthevalue,tothenearesthundreddollars,ofthecarwhen$t=4$?

• A. 5,400$
• B. 5,500$
• C. 5,600$
• D. 6,400$
• E. 7,000$

Answer 1

The correct option is C 5,600$

Considering time =$x$

and value=$v\left(f\right)=y$

We have $n=4$

$\sum =8,\sum x^2=30$

$\sum y=41900,\sum xy=49800$

$b=\frac{n\sum xy-\sum x\sum y}{n\times \sum x^2-(\sum x{)}^2}$

=$\frac{4\times 49800-8\times 41900}{4\times 30-(8{)}^2}$

$b\approx -2428.574$

$a=\frac{\sum y-b\sum x}{n}=15332.148$

Therefore, $y=a+bx=15332.148-2428.574x$

Now , $y=a+bt=15332.148-2428.574t$

at $t=4$

$y\approx$5600$