In your response to your peer’s initial post comment on other variables that might potentially confound the relationship between the two displayed variables.
Simple linear regression analyses provide a broader scope of information than correlations do. In conducting a simple linear regression, researchers are provided with several values including the slope, y-intercept, r-squared and p-value.1 In a correlation, researchers are interested in the r and p-values and these are used to determine if two variables are associated with one another, or not. Simple linear regressions assist researchers in analyzing the actual line drawn through a correlation scatterplot which can be used to predict outcomes of additional participants.
For this assignment, I am investigating the relationship between life expectancy (dependent variable) and per capita income (independent variable) in 2015. The following values were gleaned from a simple linear regression analysis conducted in Stata:
Slope = .00013
Y-Intercept = 72.42
R-squared = 0.415
The slope value tells us that for every change observed in per capita income, we can expect to see a change of .00013 in life expectancy. The y-intercept provides that with a per capita income of zero, we can expect life expectancy to be 72.42 years. The r-squared value tells us that 41.5% of the variability observed in life expectancy is due to per capita income level. Finally, the p-value tells us that we can reject the null hypothesis.1 Hypotheses in this case are as follows:
H0: Slope value = 0
H1: Slope value does not equal 0
In summary, we can use these values to predict life expectancy, given we have data for income per capita. For example, if we know a countryâ€™s per capita income in 2015 was $20,000 we can use the following equation to determine life expectancy:
Life Expectancy = 72.42 + .00013(20000)
Life Expectancy = 75.02 years