Help please with regression question

Question

Can someone please help me with this regression question. I just dont understand. We just did a project over this and I know how to get the regression equation that was given below and i know how to get r2 all while using excel but I dont know what equation this is referring to in order to get to the nearest tenth. I have tried to google all that i can with this question for help and honestly i have found nothing that helps me. Any help understand would be grand. Also say on a graph the regression line no matter the direction is plotted more close than apart would that make its strength of the linear relationship to be very strong or would the r2 number have to be a negative number for the strength to be strong.

 

 

 

The regression line is y = 0.1783x – 279.92, where x = birth year and y = U.S. life expectancy, in years. The value of r2 is 0.9748.

(a) Use the regression line to estimate the U.S. life expectancy of a baby born in 1964, to the nearest tenth of a year.


(b) Use the regression line to predict the U.S. life expectancy of a baby born in 2016, to the nearest tenth of a year.


(c) What is the slope of the regression line and what are the units of measurement?


(d) What is the value of the correlation coefficient, r?

 

 

Answer 1

Hi Lindsay,

 

a) You will have to substitute 1964 into the equation where the x is:

 

y = 0.1783(1964) - 279.92

y = 350.1812 - 279.92

y = 70.2612

so, 70.3 years old

 

b) You can solve 2016 the same way

 

c) Since this is in slope-intercept form, you can see that the slope is 0.1783 and it is measured in life expectancy per birth year

 

d) The correlation coefficient is the square root of r2 (r²), so you can work that out on a calculator.

 

In answer to your question in the narrative, the variance r2 can never be negative, even if the r value is negative.

Answer 2

Hi Lindsay,

 

We are given the regression equation: y = 0.1783x – 279.92, where x = birth year and y = U.S. life expectancy, in years and we are given the coefficient of variation or R^2 = 0.9748.

 

 (a) Use the regression line to estimate the U.S. life expectancy of a baby born in 1964, to the nearest tenth of a year.

 

y= 0.1783x – 279.92 where x= 1964; therefore y= 0.1783*(1964)- 279.92 = 70.26 years

 

(b) Use the regression line to predict the U.S. life expectancy of a baby born in 2016, to the nearest tenth of a year.

 

We use the same equation except we substitute 2016 for 1964

  

y= 0.1783*(2016) - 279.92 = 79.53 years

 

(c) What is the slope of the regression line and what are the units of measurement?

 

The slope of the regression line is the value of the coefficient of the independent variable or  0.1783. The meaning of the slope is for a 1 year change in birth year, the life expectancy changes by 0.1783 years.

 

d) What is the value of the correlation coefficient, r?

 

The correlation coefficient, r is found by taking the square root of the R^2 and calculating the sign by taking the sign of the slope. The square root of R^2 of  0.9748 is 0.9873 and since the sign of the slope is positive, the r =  0.9873 

 

Hope this helps.