b The slope shows you how the y-value changes as the x-value increases by 1. What does this mean in terms of the dependent and independent variables for this particular exercise?
C
c Remember, the first data point at 1998 equals x=8.
A
a y=10.5x+88.2
B
bSlope: 10.5
Explanation: See solution.
C
c y-intercept: 88.2
Explanation: See solution.
Practice makes perfect
a We are given a table for the number of U.S. computer and video game units sold per year.
U.S. Computer and Video Game Unit Sales
Year
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Unit Sales (millions)
152.4
184.5
196.3
210.3
225.8
240.9
249.5
229.5
241.6
267.9
To find the equation of the line of best fit, we have to perform a linear regression on our data points. Before we can do that though, we have to enter the data points into lists. We will press STAT and choose the EDIT menu. Then we will press ENTER for the first option, Edit. We can proceed with filling out the first two lists.
Next, we press the button STAT and choose CALC. In this menu, you will see all the different regressions that are available. The regression we want to perform is under the fourth option, LinReg(ax+b). By scrolling down to the fourth option and pressing ENTER twice, the calculator performs a linear regression.
Therefore, y=10.5x+88.2 is the line of best fit.
b The slope of the line of best fit is the coefficient of x.
y= 10.5x+88.2
To analyze this, we have to understand what the line of best fit describes. It describes the number of computer and video games sold in millions of units in a given year. A slope of 10.5 means that for each consecutive year, the number of sold computer and video game is expected to increase by 10.5 million units.
c The y-intercept is the equation's constant value.
y=10.5x+ 88.2
For this particular exercise, this can be interpreted as the number of computer and video games sold when x=0. If 1998 represents x=8, the year when x=0 is 1990. Therefore, the y-intercept tells us that in the year 1990 an estimated 88 million computer and video games were sold.
