drivers of that Age - ]]], [16 – 17,1,55], [18 - 19,2,30], [20 - 24, 3, A traffic safety organization has compiled data in an urban region of Canada on the rate of non-fatal vehicle injury accidents, y, as a function of the age of the driver, x. The data is shown below. It is assumed that an injury accident affects either the driver or passengers or others external to the vehicle and does not result in death. Age Range of x, Designated Age Driver Category of Driver y, Number of Injury Accidents per 10 million km driven by drivers of that Age 16-17 1 55 18-19 2 30 20-24 3 24 25-29 4 22 30-39 5 14 40-49 6 13 50-59 7 12 60-69 8 10 70-79 9 14 10

A scientist is calibrating a laboratory apparatus that will be used to measure the concentration of ozone in air samples. To check the calibration, samples of known concentration are measured. The true concentrations in ppm (x) and the measured concentrations in ppm (y) data points are:  (0, 1), (10, 11), (20, 21), (30, 28), (40, 37), (50, 48), (60, 56), (70, 68), (80, 75), (90, 86), (100, 96).  Because of random error, repeated measurements on the same sample will vary. The apparatus is considered to be in calibration if its mean response is equal to the true concentration.  To check the calibration, the linear model y = ß0 + ß1 + ε is fit. Ideally, the value of ß0 should be 0 and the value of ß1 should be 1. The least-squares estimate of the error standard deviation σ is closest to:

Imagine that a professor of psychology has two teaching assistants (TAs) who will help her grade assignments for the duration of the semester. The professor wants to make sure that she and the TAs are well calibrated with one another, so she has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, she first converts the students’ scores to z-scores for each grader. The following table shows the z-scores for a population of 10 students in her class for each grader.   Professor Teaching Assistant #1 Teaching Assistant #2 Student 1 0.70 1.27 1.27 Student 2 0.83 -0.64 -1.55 Student 3 -0.98 0.38 -0.14 Student 4 2.21 0.80 0.92 Student 5 -0.54 -1.34 -1.06 Student 6 0.43 0.10 0.30 Student 7 -1.03 -2.09 -1.50 Student 8 -0.01 0.85 1.14 Student 9 -0.54 0.48 0.57 Student 10 -1.07 0.20 0.04   The professor is going to use the z-scores to calculate the correlation coefficient between her scores…

You were asked to help with an analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers’ AGE at birth (continuous variable in years), mothers’ current HOUSING status (“own” and “not-own”; “own” is the reference group),  and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “Staten Island”; “Manhattan” is the reference group). Write down the population model that estimates the effect of mother’s AGE on BW while adjusting for mother’s current HOUSING status. If you use dummy or binary variables, specify what they mean. Write down the population model that estimates the effect of mother’s AGE on BW while adjusting for mother’s current HOUSING status and BOROUGH. If you use dummy or binary variables, specify what they mean. Write down the population model that estimates the effect of mother’s AGE…

The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. Mean Temperature (x) Net Directionality (y)   6.22 −0.08   8.01   0.25   8.67 −0.14 10.61   0.00 12.5   0.08 11.94   0.03 12.55 −0.07 17.93   0.29 18.34   0.23…

Researchers were interested in assessing whether stress levels at the beginning of the semester are related to (i.e., correlated with) stress levels during finals week. To test this, stress was measured in 5 students at the start of the semester and then again at the end of the semester during finals week.     Participant Stress 1 Stress 2 (X - MX) (Y - MY)  (X - MX) (Y - MY) (X - MX)2 (Y - MY)2  1 22 22 -4.4 -6       2 32 34 5.6 6       3 24 25 -2.4 -3       4 28 30 1.6 2       5 26 29 -0.4 1         What is the observed correlation coefficient (i.e., r value)?

Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin, - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team===== "Brooklyn Nets" . Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1459.95122 1 80 190.65061 None of the above 81 206.320988 Coef. Std. Err. 8.439024 3.049595 -5.219512 2.156389 MS t Number of obs F(1, 80) Prob > F R-squared O The Nets lost more games than they won in 2014 P>|t| 2.77 0.007 -2.42 0.018 Adj R-squared = Root…

This dataset of size n - 51 is for the 50 states and the District of Columbia in the United States. The variables are - year 2002 birth rate per 1000 females 15 to 17 years old and z- poverty rate (the percent of the state's population living in households with in- comes below the federally defined poverty level) i- 13.1 - 22.3 R- 51, Su - E(-2) - 914.7 S, - E( -2)( - 6) - 1, 256.2 Su - E(m - M) - 3, 249 SSE - E(w - - 1, 509.6 1. Find A. A and r. 2. Write the fitted linear regression model for ý, in terms of z, A, and A- For A and , use the values you obtained in problem 1. 3. Interpret the slope of the least squares line based on the context. 4. Find SST, SE and SSR. 5. Find R* and . 6. Complete a chart for ANOVA df MS pvalue Source Regression Error Total 7. Complete a chart for Parameter Estimates. t-value pvalue Parameter Intercept Slope Estimate S.e. 8. What is the residual e, for the observation (.) - (20.1,31.5)? 9. What is the conclusion for the test Ha : -0 vs Ho : +0 with a -…

Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin; - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team==== "Brooklyn Nets" Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1 80 Coef. Std. Err. MS 81 206.320988 8.439024 3.049595 -5.219512 2.156389 1459.95122 190.65061 t Number of obs F (1, 80) Prob > F R-squared. Adj R-squared = Root MSE P>|t| 2.77 0.007 -2.42 0.018 82 7.66 0.0070 0.0874 0.0760 13.808 [95% Conf. Interval]…