Activity #3: Regression Estimates
In collecting data on the Fun Size Bags of M&Ms, we also recorded the number of
M&Ms contained in the bags in addition to the total weight of the bag. Can we use the
number of M&Ms in each bag to predict the total weight of the bag? Below is a
scatterplot of the number of M&Ms and the total weight of each bag. The line is the
regression line relating the number of M&Ms to the total weight of the bag. The equation
for the regression line is: Predicted Total Weight=2.6373+0.7773*Number. The residual
plot for this regression is also given below.
1. Describe the general relationship between the number of M&Ms in each bag
and the total weight of the bag. Does it appear this relationship is strong or
weak?
2. Using the regression equation, find the predicted total weight of a bag of
M&Ms if the bag contains 21 M&Ms.
3. Calculate the residual for the bag with 21 M&Ms and a total weight of 20
grams.
4. Study the residual plot. Describe what you see and how this might affect (or
not affect) the least squares regression of the two variables.
5. Give the value of the intercept for this regression. Give the interpretation of
the intercept value in the context of the problem.
6. Look closely at the interpretation of the intercept value. What quantity does
the intercept estimate? Does this value seem reasonable given the data?
Explain your answer.
7. Give the value of the slope for this regression. Give the interpretation of the
slope value in the context of the problem.
8. Look closely at the interpretation of the slope value. What quantity does the
slope estimate? Does this value seem reasonable given the data? Explain
your answer.
9. Why do the slope and intercept not estimate these quantities well?
10. What could you do to solve this problem?