Make sure to include the unit of the values whenever appropriate.
Hint: The variables are available in the gapminder data set from the gapminder package. Note that the data set and package both have the same name, gapminder.
library(tidyverse)
options(scipen=999)
data(gapminder, package="gapminder")
houses_lm <- lm(lifeExp ~ gdpPercap,
data = gapminder)
# View summary of model 1
summary(houses_lm)
##
## Call:
## lm(formula = lifeExp ~ gdpPercap, data = gapminder)
##
## Residuals:
## Min 1Q Median 3Q Max
## -82.754 -7.758 2.176 8.225 18.426
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 53.95556088 0.31499494 171.29 <0.0000000000000002 ***
## gdpPercap 0.00076488 0.00002579 29.66 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.49 on 1702 degrees of freedom
## Multiple R-squared: 0.3407, Adjusted R-squared: 0.3403
## F-statistic: 879.6 on 1 and 1702 DF, p-value: < 0.00000000000000022Hint: Your answer must include a discussion on the p-value.
The coefficient is statistically significant because it’s p-value is less than 5% at 0.0000000000000002.
Hint: Discuss both its sign and magnitude.
With gdpPercap’s coefficient being .00076488, this results in gdpPercap increasing by $1 and the life expectancy of the individual increases by .00076488 years.
Hint: Provide a technical interpretation.
With the intercept’s value being 53.955, this means that if you’re born with a $0 gdpPercap, your life expectancy from birth is 53.95 years.
Hint: This is a model with two explanatory variables. Insert another code chunk below.
data(gapminder, package="gapminder")
houses_lm <- lm(lifeExp ~ year, gdpPercap,
data = gapminder)
# View summary of model 1
summary(houses_lm)
##
## Call:
## lm(formula = lifeExp ~ year, data = gapminder, subset = gdpPercap)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.221 -9.436 1.517 11.201 21.581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -573.69800 56.15343 -10.22 <0.0000000000000002 ***
## year 0.31998 0.02837 11.28 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.86 on 580 degrees of freedom
## (1122 observations deleted due to missingness)
## Multiple R-squared: 0.1799, Adjusted R-squared: 0.1784
## F-statistic: 127.2 on 1 and 580 DF, p-value: < 0.00000000000000022Hint: Discuss in terms of both residual standard error and reported adjusted R squared.
In the first model, the residual standard error is 10.49 but in the second model, the residual standard error is 11.86. What this means is that the first model misses about 11 people, while the second model misses about 12 people. The R-squared value in the first model is .3403 and the second models is .1784. These two values mean that the first models data points are going to be further to the line of regression than the second models. With these numbers, I’d say the second model is better because even though the first model misses less people, the second models data points will be closer to the line of regression.
Hint: Discuss both its sign and magnitude.
With the coefficient of year being .31998, for every year someone is born after 1952, their life expectancy increases by .31998 years.
Hint: We had this discussion in class while watching the video at DataCamp, Correlation and Regression in R. The video is titled as “Interpretation of Regression” in Chapter 4: Interpreting Regression Models.
Based on the numbers in the second model, the predicted life expectancy for a country with a gdpPercap of $40,000 in the year 1997 is 76.49 years.
Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.