Question

The number of VHS movie rentals has declined since the year 2000 due to the popularity of DVDs, as the following table shows. Use a graphing calculator to determine the exponential regression equation that best fits the VHS rental data. Let x represent the number of years since 2000.

Answer 1

The correct option is C.

Explanation:

The required formulas are:

1.
`\overline{x}=\frac{\sum{x}}{n}`

2.
`\overline{\ln y}=\frac{\sum{\ln y}}{n}`

3. Tread line is

`y=AB^x`

Where,
`B=e^{(S_(xy))/(S_(xx))}` and
`A=e^{\overline{\ln y}-\overline{x}\ln B}`

4.
`S_(xx)=\frac{\sum({x-\overline{x}})^2}{n}`

5.
`S_(xy)=\frac{\sum({x-\overline{x}})(\ln y-\overline{\ln y})}{n}`

The values of x and y are

x : 0 1 2 3 4 5 6

y : 10.5 7.8 6.3 5.1 4.4 3.6 3.1

Using the above formulas,

mean of x=3

mean of
`y=5.372635247`

`A=9.75319281`

`B=0.819747654`

Therefore the exponential regression equation of the line is

`y=9.75(0.8197)^x`

Therefore option C is correct.

Answer 2

Explanation:

Given that x is no of years from 2000

So x takes values as 0,1,2....6

Take the corresponding values in y.

No. x y

1 0 10.5

2 1 7.8

3 2 6.3

4 3 5.1

5 4 4.4

6 5 3.6

7 6 3.1

Mean of x =3

Mean of y = 5.372

r = correlation coeff =-0.9944

So best fit would be

`y=AB^(x) ,where A=9.753 and B=0.8197`

Hence OPtion C is right answer.