# Simple linear regression | Mathematics homework help

Category: Mathematics

In your response to your peer’s initial post comment on other variables that might potentially confound the relationship between the two displayed variables.
Peer response
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
P= 0.0000
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

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