Question

The following table presents data on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed Western countries. WINE CONSUMPTION AND HEART ATTACKS Heart divae Country 131 24 Denmark United Sues Wea German 79 Answer each question/complete the tasks. (point value is in parentheses) 1. What is the explanatory variable and what is the response variable? (2) 2. Make a complete scatterplot of the data. (3) 3. Does it appear that there is a linear relationship between alcohol consumption and heart attacks? Is there a positive association or negative association? (2) 4. Compute the equation for the least squares regression equation and the correlation coefficient. (3) 5. Write sentences that interpret the slope and y-intercept of the LSRL. (4) 6. Superimpose the regression equation on the scatterplot. (1) 7. Predict the rate of heart attacks for a country where the average wine consumption is 3 liters/person/year. (2) 8. Would it be appropriate to try to predict the death rate from heart attacks for Estonia where the per capita wine consumption is 15 liters/year? Why or why not? (2) 9. What is the explained variation for this data? Interpret your result. (3) 10. Create a residual plot and comment on what you see. (4) 11. Is there statistical evidence that a linear relationship exists between wine consumption and the occurrence of heart attacks? Conduct an appropriate test. (4)

Answer 1

$1.~Explanatory~variable=Average~wine~consumption\\ Response~variable=Rate~of~heart~attack\\ 2.$

Scatterplot of Death rate vs Wine Consumption 300 250 o 200 150 100 4 7 2 3 8 9 Wine Consumption

3. From the scatter plot it is observed that there is a linear relationship between alcohol consumption and heart attacks. Since from scatter plot it is also observed that if wine consumption increases then rate of heart attack decreases hence it is negative association.

4.

The regression equation is
Death rate = 260.56 - 22.97 Wine Consumption

Pearson correlation of Wine Consumption and Death rate = -0.843

5. Slope: If the average wine consumption is increased by one liter then the predicted rate of heart attack decreased by 0.0002297.

Intercept: When the average wine consumption is zero then  the predicted rate of heart attack is 0.0026056.

6.

Scatterplot of Death rate vs Wine Consumption 300 250 200 150 100 4 7 2 3 8 9 Wine Consumption

7. Predicted rate of heart attack when average wine consumption=1.5 liters/year= (260.56 - 22.97*1.5)/100000=0.0023.