BackFinding the Equation of the Regression Line
In Exercises 9 and 10, use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
[IMAGE]
Effects of an Outlier Refer to the Minitab-generated scatterplot given in Exercise 9 of Section 10-1
a. Using the pairs of values for all 10 points, find the equation of the regression line.
Effects of Clusters Refer to the Minitab-generated scatterplot given in Exercise 10 of Section 10-1.
a. Using the pairs of values for all 8 points, find the equation of the regression line.
Dummy Variable Refer to Data Set 18 “Bear Measurements” in Appendix B and use the sex, age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response variable represent weight, use the variable of age and the dummy variable of sex to find the multiple regression equation. Use the equation to find the predicted weight of a bear with the characteristics given below. Does sex appear to have much of an effect on the weight of a bear?
Female bear that is 20 years of age
Male bear that is 20 years of age
Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.
[IMAGE]
Fixed Percentage If a restaurant were to change its tipping policy so that a constant tip of 20% of the bill is added to the cost of the dinner, what would be the value of the linear correlation coefficient for the paired amounts of dinners/tips?
Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.
[IMAGE]
Change in Scale Exercise 1 stated that for the given paired data, r = 0.846. How does that value change if all of the amounts of dinners are left unchanged but all of the tips are expressed in cents instead of dollars?
Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.
[IMAGE]
c. What horrible mistake would be easy to make if the analysis is conducted without a scatterplot?
In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.
[Image]
Testing for Bias Can the runs test be used to show the proportion of Republicans is significantly greater than the proportion of Democrats?
In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.
[Image]
Notation Identify the values of n1,n2 and G that would be used in the runs test for randomness.
Control Limits In a control chart, what are upper and lower control limits, and what is their purpose?
Sum of Squares Criterion In addition to the value of another measurement used to assess the quality of a model is the sum of squares of the residuals. Recall from Section 10-2 that a residual is (the difference between an observed y value and the value predicted from the model). Better models have smaller sums of squares. Refer to the U.S. population data in Table 10-7.
a. Find the sum of squares of the residuals resulting from the linear model.
Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.
[IMAGE]
Scatterplot Construct a scatterplot and comment on the pattern of points.
Pepsi Cans. In Exercises 5–8, refer to the axial loads (pounds) of aluminum Pepsi cans that are 0.0109 in. thick, as listed in Data Set 41 “Aluminum Cans” in Appendix B. An axial load of a can is the maximum weight supported by the side, and it is important to have an axial load high enough so that the can isn’t crushed when the top lid is pressed onto the top. There are seven measurements from each of 25 days of production. If the 175 axial loads are in one column, the first 7 are from the first day, the next 7 are from the second day, and so on, so that the “subgroup size” is 7.
Pepsi Cans: Run Chart Treat the 175 axial loads as a string of consecutive measurements and construct a run chart. What does the result suggest?
Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.
Quarters: Notation Find the values of x(doublebar) and Rbar. Also find the values of LCL and UCL for an R chart.
Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.
Quarters: R Chart Treat the five measurements from each day as a sample and construct an R chart. What does the result suggest?