The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.
| Year | Sales ($millions) |
|---|---|
| 1993 | 315 |
| 1994 | 322 |
| 1995 | 328 |
| 1996 | 340 |
| 1998 | 345 |
| 1999 | 363 |
Let x represent the year and y represent the amount of sales, in millions of dollars, in the regression equation: [tex]y=7.36 x-14,354.33[/tex]. Use the regression equation to predict the sales of skin diving and scuba equipment in the year 2008.
A. $44,000,000
B. $440,000,000
C. $42,455,000
D. $424,550,000
Answer (2)
Substitute x = 2008 into the regression equation: y = 7.36 x − 14354.33 .
Calculate y = 7.36 ( 2008 ) − 14354.33 = 424.55 .
Multiply by 1 , 000 , 000 to convert millions of dollars to dollars: 424.55 × 1 , 000 , 000 = 424 , 550 , 000 .
The predicted sales in 2008 is 424 , 550 , 000 .
Explanation
Understanding the Problem We are given a regression equation y = 7.36 x − 14354.33 that models the sales of skin diving and scuba equipment, where x represents the year and y represents the sales in millions of dollars. We want to predict the sales for the year 2008.
Substituting the Value of x To predict the sales for the year 2008, we substitute x = 2008 into the regression equation: y = 7.36 ( 2008 ) − 14354.33
Calculating the Value of y Now, we calculate the value of y :
y = 7.36 × 2008 − 14354.33 = 14778.88 − 14354.33 = 424.55 Since y is in millions of dollars, the predicted sales in dollars is: 424.55 × 1 , 000 , 000 = 424 , 550 , 000
Final Answer Therefore, the predicted sales of skin diving and scuba equipment in the year 2008 is $424,550,000.
Examples
Regression equations are used to predict future trends based on historical data. For example, a store owner might use a regression equation to predict sales for the next year based on sales data from previous years. This helps them make informed decisions about inventory and staffing.
The predicted sales of skin diving and scuba equipment in the year 2008 is $424,550,000 based on the regression equation. By substituting 2008 into the equation and performing the calculations, we find that sales in millions convert to a total of $424,550,000. Therefore, the correct option is D: $424,550,000.
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