Math 2311 Written Homework 7 (Sections 5.4 – 5.6)

Name: PeopleSoft ID:

Instructions: • Homework will NOT be accepted through email or in person. Homework must be submitted through

CourseWare BEFORE the deadline. • Print out this file and complete the problems. • Print out this file use or software and complete the problems. • Write in black ink or dark pencil or type your solutions in the space provided. You must show all work

for full credit. • Submit this assignment at http://www.casa.uh.edu under "Assignments" and choose hw7. • Total possible points: 15

1. Section 5.4, Problem 2

2. Section 5.4, Problem 3

3. Section 5.5, Problem 2

4. Section 5.5, Problem 3

5. In R Studio use the data cars to determine the following. Hint: The data set is already in R studio use the quick reference guide to determine the following. [In R Studio, use command(file$column), such as mean(cars$speed)] Description: The data gives the speed of cars and the distances taken to stop. Note that the data were recorded in the 1920s. Format

A data frame with 50 observations on 2 variables.

speed numeric Speed (mph) dist numeric Stopping distance (ft)

a. Give a scatter plot of the data. Determine the form, direction and strength of the relationship between speed and stopping distance (dist).

b. Determine the LSRL for predicting stopping distance based on speed of the car. c. Interpret the slope of this LSRL equation. d. Determine the correlation. Give an interpretation of the correlation. e. Determine the coefficient of determination, R2. Give an interpretation of R2. f. One of the cars was going 25 mph and had a stopping distance of 85 feet. Determine the residual of this car.

6. Section 5.6, Problem 4

For problems 7 – 10 circle the best answer. 7. In the least-squares regression line, the desired sum of the errors (residuals) should be

a. positive b. negative c. zero d. maximized

8. Suppose that a least squares regression line equation is ˆy = 1.65 − 2.20x and the actual y value corresponding to

x = 10 is −19, what is the residual value corresponding to y = −19? a. 1.35 b. −1.35 c. 2.10 d. −2.10

9. A prediction of the world’s population in the year 2088 is an example of _________.

a. An outlier b. Seasonality c. Extrapolation d. Correlation

10. An observation that causes the values of the slope and the intercept in the line of best fit to be considerably different from what they would be if the observation were removed from the data set is said to be

a. A causation variable b. Extrapolation c. Influential d. A residual