Simple Linear Regression

1. What assumptions do you make when using the method of least squares to estimate a population regression line?
2. Why is it dangerous to extrapolate the estimated linear regression line outside the range of the observed values?
   An instructor asked her students to keep track of how much time each spent studying a chapter on regression in her statistics course. She collected the information together with test scores from that chapter’s test. Assume we would like to model the test grades using the information on study time, using a simple linear regression.
3. Show your (by hand) calculations for the estimate of the intercept, a in (y= a+bX).
4. Show your (by hand) calculations for the estimate of the slope, b in (y= a+bX).
   
   Your previous homework (on correlation analysis) included data on the percentage of children immunized against diphtheria, pertussis, and tetanus (DPT) in a given country and the corresponding mortality rate for children under 5. Using the same data, and with the help of statistical software, answer the following questions:
   Nation % Immunized Mortality Rate per 1000 live births
   Bolivia 77 118
   Brazil 69 65
   Cambodia 32 184
   Canada 85 8
   China 94 43
   Czech Rep. 99 12
   Egypt 89 55
   Ethiopia 13 208
   Finland 95 7
   Greece 54 9
   Japan 87 6
   Senegal 47 145
   Turkey 76 87
   UK 90 9
5. Compute the least-square regression line and interpret the estimated slope and intercept. What do they mean in words?
6. At the 0.05 level of significance, test the null hypothesis that the true population slope β is equal to 0. What do you conclude?
7. What is the 95% Confidence Interval of the slope (your software output should report it)?
8. Does the least-square regression model seem to fit the observed data? Comment on the coefficient of determination.

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