Question

The following table shows data on average per capita coffee consumption and heart disease rate in a random sample of 10 countries.

Yearly coffee consumption in liters	2.5	3.9	2.9	2.4	2.9	0.8	9.1	2.7	0.8	0.7
Death from heart diseases	221	167	131	191	220	297	71	172	211	300

1. Enter the data into your calculator and make a scatter plot.
2. Use your calculator’s regression function to find the equation of the least-squares regression line. Add this to your scatter plot from part a.
3. Explain in words what the slope and y-intercept of the regression line tell us.
4. How well does the regression line fit the data? Explain your response.
5. Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.
6. Do the data provide convincing evidence that there is a linear relationship between the amount of coffee consumed and the heart disease death rate? Carry out an appropriate test at a significance level of 0.05 to help answer this question.

Answer 1

Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

a.

b. the linear equation is : y^ = -23.878*X + 266.63

scatter plot is in the image above

c. slope: Per increase in the coffee consumption, the death from heart disease decreases by 23.878 units

Intercept: if there wasn't any coffee consumption then the death from heart disease will be 266.63

*higher coffee consumption reduces death from heart diseases

d. With a moderately good R-square of 69.8% and a p-value of less than .05, it can be concluded that linear regression is statistically significant. So, this linear regression equation has predictive power

e. The error is y-y^, which is -217.3 in 1 case, this is an outlier but not an influential point as it doesn't change the slope of the line much.

f. Yes, it does, with a p-value of less than .0025, we can say that linear regression is statistically significant.

We carried out the Linear regression exercise test above, to prove the same.