Fitting a straight line to a set of data yields the following:
1. Fitting a straight line to a set of data yields the following prediction line:
a. Interpret the meaning of the Y intercept,
b. Interpret the meaning of the slope,
c. Predict the value of Y for X =6
2. Starbucks Coffee Co. uses a data-based approach to improving the quality and customer satisfaction of its products. When survey data indicated that Starbucks needed to improve its package sealing process, an experiment was conducted (data extracted from L. Johnson and S. Burrows, "For Starbucks, It's In the Bag," Quality Progress, March 2011, pp. 17-23) to determine the factors in the bag-sealing equipment that might be affecting the ease of opening the bag without tearing the inner liner of the bag. One factor that could affect the rating of the ability of the bag to resist tears was the plate gap on the bagsealing equipment. Data was collected on 19 bags in which the plate gap was varied. The results are stored in Starbucks.
a. Construct a scatter plot.
b. Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1
c. Interpret the meaning of the slope, b1, in this problem.
d. Predict the tear rating when the plate gap is equal to 0.
Tear Viscosity Pressure Plate Gap
0.00 350.00 180.00 0.00
0.00 350.00 170.00 0.00
0.45 319.00 186.00 1.80
0.85 380.00 174.00 1.80
0.35 350.00 180.00 0.00
0.30 300.00 180.00 0.00
0.70 400.00 180.00 0.00
1.90 350.00 190.00 0.00
0.25 350.00 180.00 0.00
0.10 319.00 186.00 -1.80
0.15 380.00 186.00 -1.80
3.90 350.00 180.00 3.00
0.00 380.00 174.00 -1.80
0.55 350.00 180.00 0.00
0.00 350.00 180.00 -3.00
0.05 319.00 174.00 -1.80
0.40 319.00 174.00 1.80
4.30 380.00 186.00 1.80
0.00 350.00 180.00 0.00
3. An agent for a residential real estate company has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data (stored in RENT).
Rent Size
950 850
1600 1450
1200 1085
1500 1232
950 718
1700 1485
1650 1136
935 726
875 700
1150 956
1400 1100
1650 1285
2300 1985
1800 1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
1750 1200
4. In Problem 2, you used the plate gap on the bag-sealing equipment to predict the tear rating of a bag of coffee (stored in ). Using the results of that problem,
a. determine the coefficient of determination, and interpret its meaning.
b. determine the standard error of the estimate.
c. How useful do you think this regression model is for predicting the tear rating based on the plate gap in the bag-sealing equipment?
5. In Problem 3, an agent for a real estate company wanted to predict the monthly rent for apartments, based on the size of the apartment (stored in). Using the results of that problem,
a. determine the coefficient of determination, and interpret its meaning.
b. determine the standard error of the estimate.
c. How useful do you think this regression model is for predicting the monthly rent?
d. Can you think of other variables that might explain the variation in monthly rent?