Question

fit a regression line to the data shown in the chart, and find the coefficient of correlation for the regression line. use the regression line to predict life expectancy in the year 2000, where x is the number of decades after 1900.

year, x	life expectancy, y years
2 (1920)	52.0 years
4 (1940)	53.6 years
6 (1960)	54.8 years
8 (1980)	55.8 years

choose the correct regression line below.
a. y = 50.18x + 0.750
b. y = 0.750x - 50.18
c. y = 50.18
d. y = 0.750x + 50.18

Explanation:

Step1: Recall the form of a linear regression line

The general form of a simple - linear regression line is $y = a+bx$, where $y$ is the dependent variable (life - expectancy in this case), $x$ is the independent variable (year), $a$ is the y - intercept, and $b$ is the slope.

Step2: Analyze the data trends

As the years ($x$) increase from 1900 to 1980, the life - expectancy ($y$) also increases. This indicates a positive slope ($b>0$).

Step3: Check the equations

Option A: $y = 50.18+0.75x$ has a positive slope of $0.75$ and a y - intercept of $50.18$. Option B has a negative slope ($y = 50.18 - 0.75x$), so it can be eliminated. Option C ($y = 50.18$) is a horizontal line with a slope of 0, so it can be eliminated. Option D has the wrong form ($y=0.75x + 50.18$ is the correct form when written as $y=a + bx$ with $a = 50.18$ and $b = 0.75$).

Answer:

A. $y = 50.18+0.75x$