Researchers wanted to study the relationship between amounts of fat, sugar, and

Question

Researchers wanted to study the relationship between amounts of fat, sugar, and carbohydrates and the amount of calories in a hamburger. They gathered relevant data about 22 "brands" of fast food hamburgers and obtained the following scatter plots: a. About how many calories would you predict for a burger that has 20 grams of fat? b. About how many calories would you predict for a hamburger that has 40 grams of carbohydrates? c. Which prediction is likely to be more accurate Why do you think this? d. Which nutrient has the weakest impact on calories? Why do you think this? e. What does the idea of strength of the correlation tell you about whether a nutrient is a good predictor of calories? f. What is the direction of the fat calories graph? What does the direction of the line tell you about the association between the amount of fat and the calories in fast food hamburgers?

Explanation / Answer

a) from the last graph, if fat weight is 20 gms then from the straight line there, the calories predicted is approx 400.

b) from the 2nd graph, if carbohydrate weight is 40 gms then from the straight line there, the calories predicted is approx 600.

c) if you compare three graphs and scatter plots of the points, then you will defintiely see that, the scatter plot of the values is all very close to the estimated regression line rather than other graphs. So, Fat vs Calorie (3rd graph) is likely to be more accurate.

d) While you compare the slope of the three staright lines in the three graphs, it is vivid that, the slope of the straight line in the first graph is more flat and less than the slope of other graphs which in turn implies that the independent variable has the least impact on calorie. So the nutrients Sugar has the weakest impact on calories.

e) As the slope of all the graphs is positive, so the correlation between calorie and independent variable(Sugar/Carbohydrate/Fat) is always positive. Also slope is proportional to correlation. Also, the graph which shows the maximum degrees of association between Observed and estimated that i.e, the more correlation between observed and estimated values is high, the more good the predictor is. Here Fat is the best predictor for calories.

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