12. Regression

In the context of linear regression using the least squares method, why is the graph shown considered a line of best fit?

In simple linear regression using the least squares method, which plot will produce a straight line if the model assumptions are satisfied?

Making Predictions

In Exercises 5–8, let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10-5. Use a 0.05 significance level.

Bear Measurements Head widths (in.) and weights (lb) were measured for 20 randomly selected bears (from Data Set 18 “Bear Measurements” in Appendix B). The 20 pairs of measurements yield xbar = 6.9 in., ybar = 214.3 lb, r = 0.879 P-value = 0.000 and y^ = -212 + 61.9x. Find the best predicted weight of a bear given that the bear has a head width of 6.5 in.

Given a linear regression equation of the form $y=a+bx$ with $b=3$ and $a=-6$, what is the predicted value of $y$ when $x=4$?

5. To predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables?

The output shown was obtained from Minitab.

c. The standard error, se, is 2.167. What is an estimate of the standard deviation of y at x=10?

In the context of linear regression using the least squares method, what does each point on the least-squares regression line represent?

Which of the following is NOT true about simple linear regression using the least squares method?

Given a set of data points, which of the following equations represents the least squares regression line ($LSRL$) for predicting $y$ from $x$?

In Problems 5–10, use the results of Problems 7–12, respectively, from Section 4.2 to answer the following questions:

d. Assuming the residuals are normally distributed, test H₀: β₁ = 0 versus H₁: β₁ ≠ 0 at the α = 0.05 level of significance.

"In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.

28. Use the regression equation found in Exercise 25.

a. x_1 = 9.0, x_2 = 0.70

b. x_1 = 3.0, x_2 = 0.25

c. x_1 = 8.0, x_2 = 0.60

d. x_1 = 5.2, x_2 = 0.46"

Explain the meaning of Legendre’s quote given.

[DATA] Graduation Rates PayScale reports statistics on colleges and universities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 11_3_24 using the file format of your choice for the version of the text you are using. The data contain the four-year cost and graduation rate for over 1300 colleges and universities. Do schools that charge more have higher graduation rates? The variable “4 Year Cost” represents the four-year cost of attending the college or university. The variable “Grad Rate” represents the percentage of incoming freshman who graduate within six years.

f. What proportion of the variability in graduation rates is explained by the cost of attending?