Question

The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995.

Year	Retail Sales
0	85.851
3	108.426
6	141.781
9	169.256
12	202.297
15	222.266

Let S(t)S(t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t)=9.44t+84.182F(t)=9.44t+84.182.

36912158090100110120130140150160170180190200210220

Use the above scatter plot to decide whether the linear model fits the data well.

• The function is a good model for the data.
• The function is not a good model for the data

Estimate the retails sales in the U. S. in 2014.  billions of dollars.
Use the model to predict the year in which retails sales will be $234 billion.

Answer 1

The scatter plot for the given data is as follows:

230 180 130 80i 8 0 12 X-Independent _ Regression Line (y 9.44x + 84.18)

All the points are very close to or on the fitted regression line. So, the function is a good model for the data.

For 1995, t =0

For 1996, t =1

For 1997, t =2

Hence, for 2014, t =2014 - 1995 =19

Substitute t =19 in the regression equation: F(t)=9.44t+84.182

So, in 2014, F(t) =9.44(19) + 84.182 =263.542

Given: F(t) =234

Substituting it in the regression equation:

234 =9.44t + 84.182

$\implies$9.44t =234 - 84.182 =149.818

$\implies$t =149.818/9.44 =15.87 (rounded to 16)

The year in which t =16 is 1995+16 =2011