Exercises: Using only the information above (i.e., you are not expected to load the data into RStudio to do any investigations), respond to the following questions. 1. Give the equation of the least...

Extracted text: Exercises: Using only the information above (i.e., you are not expected to load the data into RStudio to do any investigations), respond to the following questions. 1. Give the equation of the least square regression line that uses a country's birth rate to predict the life expectancy of its citizens. 2. Use your linear model from part 1. to predict the life expectancy in a country with a birth rate of 36 per 1000 people. 3. Guinea-Bissau has a birth rate of 36 per 1000 people and a life expectancy of 57.8 years. Use the answer in part 2. to find the residual for this data point. 4. Is there evidence that birth rate is an effective predictor of life expectancy? Carry out the calculation of the p-value to make an assessment. (Show your work.) 5. Find the 99% confidence interval for the slope of the true linear model and interpret the interval. 6. Using the R output above, determine the value of the correlation coefficient. What does this value tell you about the linear relationship between life expectancy and birth rate?

LifeBirth.lm <-lm (lifeexpectancy~birthrate,="" data="SampCountries)"> summary (LifeBirth. lm) Call: Im (formula = LifeExpectancy BirthRate, data = SampCountries) Residuals: Min 10 Median 30 Маx -7.0592 -2.3047 0.9123 2.5019 5.8358 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 85.26295 1.03301 82.54 BirthRate -0.63291 0.04492 -14.09 Residual standard error: 3.424 on 48 degrees of freedom Multiple R-squared: 0.8053, Adjusted R-squared: 0.8012 F-statistic: 198.5 on 1 and 48 DF, p-value: < 2.2e-16="" lifeexpectancy="" "/="">
Extracted text: Consider trying to predict the life expectancy of citizens in a country based on the birth rate (per 1000 people) in that country. Here is a scatterplot of the data from a random sample of 50 countries. > ggplot (SampCountries, aes (BirthRate, LifeExpectancy)) + geom_point (color = "darkred")+ labs (title = "Life Expectancy by Birth Rate") + Life Expectancy by Birth Rate 80 - 70 - 10 20 30 40 BirthRate Here is (some of) the R output for the linear model for this data. > LifeBirth.lm <-lm (lifeexpectancy~birthrate,="" data="SampCountries)"> summary (LifeBirth. lm) Call: Im (formula = LifeExpectancy BirthRate, data = SampCountries) Residuals: Min 10 Median 30 Маx -7.0592 -2.3047 0.9123 2.5019 5.8358 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 85.26295 1.03301 82.54 BirthRate -0.63291 0.04492 -14.09 Residual standard error: 3.424 on 48 degrees of freedom Multiple R-squared: 0.8053, Adjusted R-squared: 0.8012 F-statistic: 198.5 on 1 and 48 DF, p-value: < 2.2e-16 lifeexpectancy 2.2e-16="">