Exam 2: Data

Another farmer has increased his wheat production by about the same percentage each year. His most useful predictive model is probably…

Researchers studying growth patterns of children collect data on the heights of fathers and sons. The correlation between the fathers' heights and the heights of their 16 year-old sons is most likely to be...

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 -The farmer with 35 had 15,400 oranges; find the value of his residual. Show your work.

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 slope of your model in context.

A plot of the residuals versus the fitted values for record-breaking times of female marathon runners for the years 1998 - 2003 is: Based on this residuals plot, does it seem reasonable to use linear regression for this model? Explain.

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 S 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 S 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 S Carat 748.10 0.16 1076.18 0.19 1289.20 0.23 1597.63 0.27 2038.09 0.32 -Interpret the intercept of your model in context.

This regression analysis examines the relationship between the number of years of formal education a person has and their annual income. According to this model, about how much more money do people who finish a 4-year college program earn each year, on average, than those with only a 2-year degree? Dependent variable is Income $R$ -squared $=25.8 \%$ $\mathrm{s}=3888$ with 57 degrees of freedom Variable Coefficient s.e. of Coeff Constant 3984.45 6600 Education 2668.45 600.1

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

On the axes below, sketch a scatterplot described: a. a strong negative association b. a strong association, but r is near 0 c. a weak but positive association

The following is a scatterplot of the average final exam score versus midterm score for 11 sections of an introductory statistics class: The correlation coefficient for these data is r = 0.829. If you had a scatterplot of the final exam score versus midterm score for all individual students in this introductory statistics course, would the correlation coefficient be weaker, stronger, or about the same? Explain.

Penicillin Doctors studying how the human body assimilates medication inject some patients with penicillin, and then monitor the concentration of the drug (in units/cc) in the patients' blood for seven hours. The data are shown in the scatterplot. First they tried to fit a linear model. The regression analysis and residuals plot are shown. Dependent variable is: Concentration No Selector R squared $=90.8 \% \quad$ R squared (adjusted) $=90.6 \%$ $s=3.472$ with $43-2=41$ degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 4900.55 1 4900.55 407 Residual 494.199 41 12.0536 Variable Coefficient s.e. of Coeff t-ratio prob Constant 40.3266 1.295 31.1 \leq0.0001 Time -5.95956 0.2956 -20.2 \leq0.0001 a. Find the correlation between time and concentration. b. Using this model, estimate what the concentration of penicillin will be after 4 hours. c. Is that estimate likely to be accurate, too low, or too high? Explain. Now the researchers try a new model, using the re-expression log(Concentration). Examine the regression analysis and the residuals plot below. Dependent variable is: LogCnn No Selector $R$ squared $=98.0 \% \quad R$ squared (adjusted) $=98.0 \%$ $s=0.0451$ with $43-2=41$ degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 4.11395 1 4.11395 2022 Residual 0.083412 41 0.002034 Variable Coefficient s.e. of Coeff t-ratio prob Constant 1.80184 0.0168 107 \leq0.0001 Time -0.172672 0.0038 -45.0 \leq0.0001 d. Explain why you think this model is better than the original linear model. e. Using this new model, estimate the concentration of penicillin after 4 hours.

A silly psychology student gathers data on the shoe size of 30 of his classmates and their GPA's. The correlation coefficient between these two variables is most likely to be

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.

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 S 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 S Carat 748.10 0.16 1076.18 0.19 1289.20 0.23 1597.63 0.27 2038.09 0.32 -Interpret the slope of your model in context.

The bigger the stop sign, the more expensive it is. Here is a graph of the height of a sign in inches versus its cost in dollars. -Describe why performing linear regression with these data is not a good decision.

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

Here is a scatterplot of weight versus height for students in an introductory statistics class.The men are coded as '1' and appear as circles in the scatterplot; the women are coded as '2' and appear as squares in the scatterplot. a. Do you think there is a clear pattern? Describe the association between weight and height. b. Comment on any differences you see between men and women in the plot. c. Do you think a linear model from the set of all data could accurately predict the weight of a student with height 70 inches? Explain.

The bigger the stop sign, the more expensive it is. Here is a graph of the height of a sign in inches versus its cost in dollars. To achieve linearity, the data was transformed using a square root function of cost. Here are the results and a residual plot.Dependent Variable: sqrt(cost) $\mathrm{R}$ (correlation coefficient) $=0.98946627$ $\mathrm{R}-\mathrm{sq}=0.97904349$ s: 0.2141 Parameter coeff se Intercept 1.1857 0.4346 height 0.1792 0.0151 -Use your equation to predict the cost of a 48" stop sign.

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 S 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 S Carat 748.10 0.16 1076.18 0.19 1289.20 0.23 1597.63 0.27 2038.09 0.32 -The correlation coefficient between the hours that a person is awake during a 24-hour period and the hours that same person is asleep during a 24-hour period is most likely to be

Height and weight Suppose that both height and weight of adult men can be described with Normal models, and that the correlation between these variables is 0.65. If a man's height places him at the 60th percentile, at what percentile would you expect his weight to be?