Solve the problem.
-Consider the data showing the average life expectancy of woman in various years. Find the regression line. Let the year 1900 represent x = 0.
A) y = 8.3x + 22.1
B) y = 0.15x + 60.9
C) y = 0.37x - 21.8
D) y = - 0.11.2x + 23.1

Question

Solve the problem.
-Consider the data showing the average life expectancy of woman in various years.  Find the regression line. Let the year 1900 represent x = 0.
A) y = 8.3x + 22.1 
B) y = 0.15x + 60.9 
C) y = 0.37x - 21.8 
D) y = - 0.11.2x + 23.1

Quizplus · Accepted Answer

We can use a calculator or statistical software to find the regression line, but one way to do it by hand is to use the formula for the slope:

slope = r(sy / sx)

where r is the correlation coefficient, sy is the standard deviation of the y values, and sx is the standard deviation of the x values. We can find these values for the given data:

x: 0   10  20  30  40  50  60  70
y: 47  50  54  60  68  73  76  79

mean x: 35
mean y: 63.5
sy: 11.67
sx: 25.82
r: 0.9814

Substituting into the formula, we get:

slope = 0.9814(11.67/25.82) = 0.441

Now we can use the formula for the y-intercept:

y-intercept = y - slope(x)

Choosing 1900 as x = 0, we get:

y-intercept = 63.5 - 0.441(0) = 63.5

Therefore, the regression line is:

y = 0.441x + 63.5

Which matches option B. To find the regression line, we need to use linear regression. We can use a graphing calculator or a spreadsheet program like Microsoft Excel to do this. Using Excel, we input the data and use the "trendline" feature to get the equation of the line. The equation we get is y = 0.15x + 60.9. Since the year 1900 represents x = 0, we can substitute 0 for x and get y = 60.9, which is the average life expectancy of women in 1900. Therefore, the best choice is B.

Solve the Problem. -Consider the Data Showing the Average Life Expectancy of Woman