Exam 2: Data

A regression equation is found that predicts the increased cost of a home owner's electricity bill Given the number of holiday lights they put on the outside of their house. The equation is dollars =2.5 + 0.02(light) . If a house has 400 lights and a $15 increase in their electricity cost, find their residual.

Match the following descriptions with the most likely correlation coefficient. The number of hours you study and your exam score. The number of siblings you have and your GPA. The number of hours you practice a task and the number of minutes it takes you to complete it. The number of hours you use a pencil and its length. A. -0.78 B. 0.13 C. 0.46 D. 0.89

Computer output in the scenario described in problem #8 reports that s = 2.3. Which is the correct interpretation of this value?

It takes a while for new factory workers to master a complex assembly process. During the first month new employees work, the company tracks the number of days they have been on the job and the length of time it takes them to complete an assembly. The correlation is most likely to be

One of your classmates is working on a science project for a unit on weather. She tracks the temperature one day, beginning at sunrise and finishing at sunset. Given that you are know for being the stats expert, she asks you about calculating the correlation for her data. What is the best advice you could give her?

Which statement about correlation is true? I. Regression based on data that are summary statistics tends to result in a higher correlation. II. If $r^{2}=0.95$ , the response variable increases as the explanatory variable increases. III. An outlier always decreases the correlation.

During a chemistry lab, students were asked to study a radioactive element which decays over time. The results are in the table. Time (in days) 0 2 4 6 8 10 Element (in grams) 320 226 160 115 80 57 a. Model the remaining mass of the element. b. Find the predicted amount of the element remaining after thirty minutes.

Which scatterplot shows a strong association between two variables even though the correlation is probably near zero?

A medical researcher finds that the more overweight a person is, the higher his pulse rate tends to be. In fact, the model suggests that 12-pound differences in weight are associated with differences in pulse rate of 4 beats per minute. Which is true? I. The correlation between pulse rate and weight is 0.33. II. If you lose 6 pounds, your pulse rate will slow down 2 beats per minute. III. A positive residual means a person's pulse rate is higher than the model predicts.

Gas mileage An important factor in the amount of gasoline a car uses is the size of the engine. Called "displacement", engine size measures the volume of the cylinders in cubic inches. The regression analysis is shown. Dependent variable is: $\quad$ $\quad$ MPG 89 total cases of which 0 are missing $\mathrm{R}$ squared $=60.9 \% \quad \mathrm{R}$ squared (adjusted) $=60.0 \%$ $s=3.056$ with $89-2=87$ degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 696.744 1 696.744 74.6 Residual 448.236 48 9.33826 Variable Coefficient s.e. of Coeff t-ratio prob Constant 34.9799 1.231 28.4 <0.0001 Eng. Displcmt -0.066196 0.0077 -8.64 <0.0001 a. How many cars were included in this analysis? b. What is the correlation between engine size and fuel economy? c. A car you are thinking of buying is available with two different size engines, 190 cubic inches or 240 cubic inches. How much difference might this make in your gas mileage? (Show your work.)

A study examined the number of trees in a variety of orange groves and the corresponding number of oranges that each grove produces in a given harvest year. Linear regression was calculated and the results are below. linear regression results: Dependent Variable: oranges Independent Variable: trees Sample size: 9 R-sq = 0.886 s = 31394.7 Parameter Estimate Std. Err. Constant 390.59 16328.8 Trees 525.84 71.22 -If these data were collected in California, would you feel confident in using this equation to make predictions about Florida orange groves also? Explain.

In an effort to decide if there is an association between the year of a postal increase and the new postal rate for first class mail, the data were gathered from the United States Postal Service. In 1981, the United States Postal Service changed their rates on March 22 and November 1. This information is shown in the table below. Year Rate 1971 0.08 1974 0.10 1975 0.13 1978 0.15 1981 0.18 1981 0.20 1985 0.22 1988 0.25 1991 0.29 1995 0.32 -Would it be better for customers for a year to have a negative residual or a positive residual from this model? Explain.

Crawling Researchers at the University of Denver Infant Study Center investigated whether babies take longer to learn to crawl in cold months (when they are often bundled in clothes that restrict their movement) than in warmer months. The study sought an association between babies' first crawling age (in weeks) and the average temperature during the month they first try to crawl (about 6 months after birth). Between 1988 and 1991 parents reported the birth month and age at which their child was first able to creep or crawl a distance of four feet in one minute. Data were collected on 208 boys and 206 girls. The graph below plots average crawling ages (in weeks) against the mean temperatures when the babies were 6 months old. The researchers found a correlation of r = -0.70 and the their line of best fit was $\hat{\text{AvAge}}$ = 36 - 0.08AvTemp. a. Draw the line of best fit on the graph. (Show your method clearly.) b. Describe the association in context. c. Explain (in context) what the slope of the line means. d. Explain (in context) what the y-intercept of the line means. e. Explain (in context) what $R^{2}$ means. f. In this context, what does a negative residual indicate?

A researcher studied the relationship between family income and amount of money spent on an automobile. She calculated that $\mathrm{R}^{2}$ = 45%. Which is the correct interpretation?

Car commercials A car dealer investigated the association between the number of TV commercials he ran each week and the number of cars he sold the following weekend. He found the correlation to be r = 0.56. During the time he collected the data he ran an average of 12.4 commercials a week with a standard deviation of 1.8, and sold an average of 30.5 cars with a standard deviation of 4.2. Next weekend he is planning a sale, hoping to sell 40 cars. Create a linear model to estimate the number of commercials he should run this week. Write a sentence explaining your recommendation.

Baseball coaches use a radar gun to measure the speed of pitcher’s fastball. They also record outcomes such as hits and strikeouts. The scatterplot below shows the relationship between the average speed of a fastball and the average number of strikeouts per nine innings for each pitcher on the Bulldogs, based on the past season. -Comment on any unusual data point or points in the data set. Explain.

Baseball coaches use a radar gun to measure the speed of pitcher’s fastball. They also record outcomes such as hits and strikeouts. The scatterplot below shows the relationship between the average speed of a fastball and the average number of strikeouts per nine innings for each pitcher on the Bulldogs, based on the past season. -Do you think the association would be stronger or weaker if we used data from one month of the season?

The correlation coefficient between high school grade point average (GPA) and college GPA is 0.560. For a student with a high school GPA that is 2.5 standard deviations above the mean, we Would expect that student to have a college GPA that is_____ the mean.

During a science lab, students heated water, allowed it to cool, and recorded the temperature over time. They computed the difference between the water temperature and the room temperature. The results are in the table. Time (in minutes) 10 20 30 40 50 60 Difference in temp. (degrees F) 68 36 20 10 6 4 -Researchers investigating the association between the size and strength of muscles measured the forearm circumference (in inches) of 20 teenage boys. Then they measured the strength of the boys' grips (in pounds). Their data are plotted below. a. Write a few sentences describing the association. b. Estimate the correlation. r =_____ c. If the point in the lower right corner (at about 14" and 38 lbs.) were removed, would the correlation become stronger, weaker, or remain about the same? d. If the point in the upper right corner (at about 15" and 75 lbs.) were removed, would the correlation become stronger, weaker, or remain about the same?

An 8th grade class develops a linear model that predicts the number of cheerios (a small round cereal) that fit on the circumference of a plate by using the diameter in inches. Their model is cheerios = 0.56 + 5.11(diameter). -The slope of this model is best interpreted in context as……