Project #3 Regression Analysis Bicycling * To be completed independently - No teams are to be used for this project. * Clearly label each answer (using bullets) to avoid confusion when grading and show your work. According to the dataset below, the mean age of cyclists killed each year during the decade from 1998 to 2010 appears to be increasing. The normal assumption is that these deaths are due to unsafe biking habits. An insurance company analyst thinks the data on ages of cyclist accident deaths are due to the entire population of cyclists getting older and having slower reaction times, not to a change in the safe riding habits of older cyclists. 1. Draw a scatterplot (or use Excel), take a screenshot (alt + print Year Mean Age screen), and paste your screenshot. 1998 32 Summarize what the scatterplot says about the trend and level of strength of the data. 1999 33 2000 35 Look for Direction: What's Look for Form: Straight, the sign-positive, negative, curved, something exotic, or 2001 36 or neither? no pattern 2002 37 Look for Strength: How Look for Unusual much scatter? Features: Are there unusual observations or subgroups? 2003 36 2004 39 3. Draw a scatterplot (or use Excel) of the residuals for the linear 2005 39 model, take a screenshot (alt + print screen), and paste your screenshot. Comment on its significance. 2006 41 2007 40 4. When examining the ages of victims in cycle/car accidents, how would you label each axis? What is the explanatory (independent) 2008 41 and response (dependent) variable? 2009 41 5. Using the data provided in item #7, what is the t-value for this 2010 42 data (write it out or use Excel)? Remember: test statistic 7 = (point estimate - null value) / SE 6. Show the calculation for the correlation coefficient and explain your answer (correct answer provided below). 7. State the degree of freedom (df) for this dataset. 8. Using the following summary statistics for the cyclist data, state the y-intercept and slope for the line of best fit (see notes on the next page). y = Bo + Bix 9. Find and interpret the R2 (coefficient of Variation) for the regression of cyclist death ages vs. time. What does the coefficient of Variation value tell us? 10. Theoretically, what is the mean age for cyclist accident deaths in 2011?Correlation and the Line The Linear Model Straight lines can be written as y = b + bix. Residuals The scatterplot of real data won't fall exactly on a line, so we A linear model can be written in the form y = by + bx denote the model of predicted values by the equation where b, and b, are numbers estimated from the data and j is the v = b +b,x. predicted value. The difference between the predicted value and the observed value, y, is called the residual and is denoted e. e = y- y To find the intercept of our line, we use the means. If our line estimates the data, then it should predict y for the x-value x. Thus, we get the following relationship from our line. y = bo + bjx We can now solve this equation for the intercept to obtain the formula for the intercept. bo = y-b,x V = 37.85; x = 2004; s, = 3.26; s, = 3.89;r = 0.96 b = r S , bo = y - b x = MeanAge = y-intercept + Slope(Year)