Question

The following table shows birthrates for babies born outside of marriage. Use the data below. Let be the birthrate percent and be the number of years since 1985.

Year Births (Percent)
1985 9.6
1990 13.15
1995 18.3
2000 22.25
2005 26.8
2010 31.05
2015 34.8

Calculate the linear regression line:


Round to the nearest hundredth.
Hint: Remember that since we are calculating years since 1985 we need to modify the values

Answer 1

The linear regression line equation for the birth rate percent for a specified number of years since 1985, obtained using the least squares method is; y = 9.4321 + 0.8564·x

The steps used to find the linear regression line equation can be presented as follows;

Let x represent the number of years since 1985 and let x represent the birth rate percent. The least squares regression line equation can be presented as follows;

y = a + b·x

`b = \frac{\sum(x - \bar{x})* (y - \bar{y})}{\sum(x - \bar{x})^2}`

The table of values indicates that we get;

`\bar{x}` = 15

`\bar{y}` = 22.27857

`\sum(x - \bar{x})* (y - \bar{y})` = 599.5

`}{\sum(x - \bar{x})^2}` = 700

b = 599.5/700

599.5/700 ≈ 0.8564

b ≈ 0.8564

`\bar{y}` = a + b·
`\bar{x}`

a =
`\bar{y}` - b·
`\bar{x}`

a = 22.27857 - (599.5/700) × 15

22.27857 - (599.5/700) × 15 ≈ 9.4321

The linear regression line equation is; y = 9.4321 + 0.8564·x