Exam 2: Exploring Relationships Between Variables

The following scatterplot shows the relationship between the time (in seconds) it took men to run the 1500m race for the gold medal and the year of the Olympics that the race was run in: a. Write a few sentences describing the association. b. Estimate the correlation. $r =$ ________

One 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?

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.

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 $\mathrm { R } - \mathrm { sq } = 0.886$ $\mathrm {~s} = 31394.7$ Parameter Estimate Std. Err. Constant 390.59 16328.8 Trees 525.84 71.22 -Interpret the slope in context.

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 chee^rios = 0.56 + 5.11(diameter). -If the diameter is increased from 4 inches to 14 inches, the predicted number of cheerios will Increase by about…

The correlation between a family's weekly income and the amount they spend on restaurant meals Is found to be $r = 0.30$ Which must be true? I. Families tend to spend about 30% of their incomes in restaurants. II. In general, the higher the income, the more the family spends in restaurants. III. The line of best fit passes through 30% of the (income, restaurant$) data points.

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 R-squared $= 76.5 \%$ $s = 383.3$ 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.

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004: 2004 US \ Carat 494.82 0.12 768.03 0.17 1105.03 0.20 1508.88 0.25 1826.18 0.28 2096.89 0.33 2004 US \ Carat 688.24 0.15 944.90 0.18 1071.75 0.21 1504.44 0.26 1908.28 0.29 2409.76 0.35 2004 US \ Carat 748.10 0.16 1076.18 0.19 1289.20 0.23 1597.63 0.27 2038.09 0.32 -What is the correlation between cost and size?

A residual plot that has no pattern is a sign that…

Variables X and Y have $r = 0.40$ 0.40. If we decrease each X value by 0.1, double each Y value, and then Interchange them (put X on the Y-axis and vice versa) the new correlation will be

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. 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 -Create a model to predict postal rates from the year.

A scatterplot of $\frac { 1 } { \sqrt { y } }$ vs. x shows a strong positive linear pattern. It is probably true that

The model $\sqrt { \hat { s t r } } = 12 + 20 \mathrm { dia }$ can be used to predict the breaking strength of a rope (in pounds) from Its diameter (in inches). According to this model, how much force should a rope one-half inch in Diameter be able to withstand?

If the point in the upper left corner of the scatterplot is removed, what will happen to the Correlation (r) and the slope of the line of best fit (b)?

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004: 2004 US \ Carat 494.82 0.12 768.03 0.17 1105.03 0.20 1508.88 0.25 1826.18 0.28 2096.89 0.33 2004 US \ Carat 688.24 0.15 944.90 0.18 1071.75 0.21 1504.44 0.26 1908.28 0.29 2409.76 0.35 2004 US \ Carat 748.10 0.16 1076.18 0.19 1289.20 0.23 1597.63 0.27 2038.09 0.32 -Would it be better for a customer buying a diamond to have a negative residual or a positive residual from this model? Explain.

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 -=0.886 =31394.7 Parameter Estimate Std. Err. Constant 390.59 16328.8 Trees 525.84 71.22 -The farmer with 35 had 15,400 oranges; find the value of his residual. Show your work.

A researcher notes that there is a positive correlation between the temperature on a summer day and the number of bees that he can count in his garden over a 5-minute time span. a. Describe what the researcher means by a positive correlation. b. If the researcher calculates the correlation coefficient using degrees Fahrenheit instead of Celsius, will the value be different?

If the point in the upper right corner of this scatterplot is removed from the data set, then what will Happen to the slope of the line of best fit (b) and to the correlation (r)?

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 chee^rios = 0.56 + 5.11(diameter). -The slope of this model is best interpreted in context as…

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