Back[DATA] The following data represent the height (inches) of boys between the ages of 2 and 10 years.
d. Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.
[DATA] Age versus HDL Cholesterol A doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good) cholesterol. He randomly selected 17 of his patients and determined their HDL levels. He obtained the following data.
b. Determine the least-squares regression equation from the sample data.
[DATA] Tar and Nicotine Every year the Federal Trade Commission (FTC) must report tar and nicotine levels in cigarettes to Congress. Tar and nicotine levels of over 1200 brands of cigarettes are given to Congress and a random sample of those appear in the following table:
e. Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line.
Notation Using the weights (lb) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in Data Set 35 “Car Data” of Appendix B, we get this regression equation:
y^ = 58.9 - 0.00749x, where x represents weight.
a. What does the symbol y^ represent?
What do the y-coordinates on the least-squares regression line represent?
The difference between the observed and predicted value of y is the error, or ________.
[DATA] The following data represent the height (inches) of boys between the ages of 2 and 10 years.
h. Explain why the predicted heights found in parts (a) and (f) are the same, yet the intervals are different.
[DATA] Putting It Together: Predicting Intelligence Can a photograph of an individual be used to predict their intelligence? Researchers at Charles University in Prague, Czech Republic, had 160 raters analyze the photos of 80 students and asked each rater to rate the intelligence and attractiveness of the individual in the photo on a scale from one to seven. To eliminate individual bias in ratings, each rater’s scores were converted to z-scores using each individual’s mean rating. The perceived intelligence and attractiveness of each photo was calculated as the mean z-score. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 12_4_19 using the file format of your choice. The following explains the variables in the data:
sex: Gender of the individual in the photo
age: Age of the individual in the photo
perceived intelligence (ALL): Mean z-score of the perceived intelligence of all 160 raters
perceived intelligence (WOMEN): Mean z-score of the perceived intelligence of the female raters
perceived intelligence (MEN): Mean z-score of the perceived intelligence of the male raters
attractiveness (ALL): Mean z-score of the attractiveness rating of all 160 raters
attractiveness (MEN): Mean z-score of the attractiveness rating of the male raters
attractiveness (WOMEN): Mean z-score of the attractiveness rating of the female raters
IQ: Intelligence quotient based on the Czech version of Intelligence Structure Test
d. Provide an interpretation of the intercept.
"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.
23. Points Earned Construct a 90% prediction interval for total points earned in Exercise 13 when the number of goals allowed by the team is 140."
Given a set of data points, the least squares regression line is calculated to best fit the data. Which of the following values is the most likely approximate slope of the line of best fit if the data shows a strong negative linear relationship?
Which of the following is true concerning linear regression using the least squares method?
[DATA] Height versus Head Circumference [See Problem 13 in Section 12.3] A pediatrician wants to determine the relation that may exist between a child’s height and head circumference. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data:
d. State your conclusion to the hypotheses from part (b).
1. Interpret the meaning of the coefficient -8.2 in the multiple regression equation y=112.1+0.43x_1-8.2x_2+29.5x_3.
Given the least squares regression equation , when , what does equal?
In Problems 5–10, use the results of Problems 7–12, respectively, from Section 4.2 to answer the following questions:
a. What are the estimates of β₀ and β₁?