Exam 2: Data

Using the equation in number #8 again, if a homeowner doubles the number of lights he uses from 500 to 1000, how much do we predict he will increase his electric bill by?

A regression analysis of students' college grade point averages (GPAs) and their high school GPAs found R² = 0.311. Which of these is true? I. High school GPA accounts for 31.1% of college GPA. II. 31.1% of college GPAs can be correctly predicted with this model. III. 31.1% of the variance in college GPA can be accounted for by the model.

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 Since $r^{2}$ is not 100%, there must be other factors in influencing the number of oranges harvested. What percentage is that and what is another factor you think might be involved?

Email At CPU every student gets a college email address. Data collected by the college showed a negative association between student grades and the number of emails the student sent during the semester. a. Briefly explain what "negative association" means in this context. b. After seeing this study the college proposes trying to improve academic performance by limiting the amount of email students can send through the college address. As a statistician, what do you think of this plan? Explain briefly.

The model $\sqrt{\hat{\text { distance }}}=3.30+0.235$ (speed) can be used to predict the stopping distance (in feet) for a car traveling at a specific speed (in mph). According to this model, about how much distance will a car going $65 \mathrm{mph}$ need to stop?

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 -Interpret the intercept of your model in context.

High Score The longer you play a video game, the higher score you can usually achieve. An analysis of a popular game found the following relationship between the hours a player has played a game and their corresponding high score on that game. Dependent variable is High Score $\text { R-squared }=76.5 \%$ $\mathrm{s}=383.3$ with 89 degrees of freedom Variable Coefficient s.e. of Coeff Constant 524.8 145.3 Hours 2498.8 324.5 a. Write the regression equation and define the variables of your equation in context. b. Interpret the slope in context. c. Interpret the y-intercept in context. d. Interpret s in context. e. What is the correlation coefficient? Interpret this value in context.

A business owner notes that for every extra hour his store is open, his total sales increase by a fixed amount. His most useful predictive model is probably……

Penicillin assimilation Doctors studying how the human body assimilates medication inject a patient with penicillin, and then monitor the concentration of the drug in the patient's blood for several hours. The data are shown in the table. Time elapsed Concentration (Hours) (Units/cc) 1 42 2 28 3 19 4 13 5 9 6 6 7 4 a. Straighten the scatterplot by re-expressing these data and create an appropriate model for predicting the concentration of penicillin. b. Use your model to estimate what the concentration of penicillin will be after 8 hours.

Put to Work Some students have to work part time jobs to pay for college expenses. A researcher examined the academic performance of students with jobs versus those without. He found a positive association between the number of hours worked and GPA. Explain what "positive association" means in this context.

Current research states that a good diet should contain 20-35 grams of dietary fiber. Research also states that each day should start with a healthy breakfast. The nutritional information for 77 breakfast cereals was reviewed to find the grams of fiber and the number of calories per serving. The scatterplot below shows the relationship between fiber and calories for the cereals. -Comment on any unusual data point or points in the data set. Explain.

A least squares line of regression has been fitted to a scatterplot; the model's residuals plot is shown. Which is true?

Which statement about residuals plots is true? I. A curved pattern indicates nonlinear association between the variables. II. A pattern of increasing spread indicates the predicted values become less reliable as the explanatory variable increases. III. Randomness in the residuals indicates the model will predict accurately.

All but one of the statements below contain a mistake. Which one could be true?

A regression model examining the amount of weight a football player can bench press found that10 cm differences in chest size are associated with 8 kg differences in weight pressed. Which is True? I. The correlation between chest size and weight pressed is r = 0.80 II. As a player gets stronger and presses more weight his chest will get bigger. III. A positive residual means that the player pressed more than predicted.

Current research states that a good diet should contain 20-35 grams of dietary fiber. Research also states that each day should start with a healthy breakfast. The nutritional information for 77 breakfast cereals was reviewed to find the grams of fiber and the number of calories per serving. The scatterplot below shows the relationship between fiber and calories for the cereals. -Do you think there is a clear pattern? Describe the association between fiber and calories.

Which statement about re-expressing data is not true? I. Unimodal distributions that are skewed to the left will be made more symmetric by Taking the square root of the variable. II. A curve in which the direction of the association changes from negative to positive will not benefit from re-expression. III. One goal of re-expression may be to make the variability of the response variable more uniform.

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 -Make a scatterplot and describe the association between the year and the first class postal rate.

Education research consistently shows that students from wealthier families tend to have higher SAT scores. The slope of the line that predicts SAT score from family income is 6.25 points per $1000, and the correlation between the variables is 0.48. Then the slope of the line that predicts family income from SAT score (in $1000 per point)…

A scatterplot of log(Y) vs. log(X) reveals a linear pattern with very little scatter. It is probably true that…