Does prison really deter violent crime? Let x represent percent change in the rate of violent crime and y represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained. x 6.5 5.5 3.5 5.2 6.2 6.5 11.1 y −1.5 −4.5 −6.2 −4.0 3.6 −0.1 −4.4    given Σx = 44.5, Σy = −17.1, Σx2 = 315.69, Σy2 = 109.27, Σxy = −104.17,  and r ≈ 0.0964.   a) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) r2 =   explained      % unexplained      % b) Considering the values of r and r2, does it make sense to use the least-squares line for prediction? Explain your answer. choose one: The correlation between the variables is so high that it makes sense to use the least-squares line for prediction. The correlation between the variables is so low that it makes sense to use the least-squares line for prediction.     The correlation between the variables is so high that it does not make sense to use the least-squares line for prediction. The correlation between the variables is so low that it does not make sense to use the least-squares line for prediction.

The correlation between hours of sleep and hours of study is r = 0.14. (a) Calculate r². (Round your answer to four decimal places.) ,2 = = (b) Choose a sentence that interprets value r². 1.96% of the variation in hours of sleep is not explained by hours of study. Variation in hours of study explains about 1.96% of the observed variation in hours of sleep. 1.96% of the variation in hours of sleep is not explained by the variation in hours of study. Hours of study explains about 1.96% of the observed variation in hours of sleep.

Rail ridership during the summer months in the North-East is believed to beclosely related to the number of tourists visiting the region. The following tableshows the data on the number of tourists and North-East ridership for the past16 years. (Answer in Excel showing formulas for answers)Year      Tourists( in millions)     Rail Ridership (in millions) 2000              9                                         2.32001              4                                         1.9 2002              7                                         1.7 2003              5                                         1.8 2004              12                                       2.8 2005              13                                       2.9 2006              14                                       2.42007              20                                       4.8 2008              7                                        1.3 2009              5                                         1.12010…

The following table presents the time taken to review articles that were submitted for publication to a particular journal during a recent year. A few articles took longer than  6 months to review; these are omitted from the table. Consider the data to be a population. Time (Months) Number of Articles −00.9 45 −1.01.9 18 −2.02.9 16 −3.03.9 17 −4.04.9 12 −5.05.9 13     (a) Approximate the variance of the times. Round the answer to at least two decimal places. The variance is    .(b) Approximate the standard deviation of the times. Round the answer to at least two decimal places.The standard deviation is    .

Utilizing the previous table: A sample of 25 cities have been classified as high or low on their homicide rates and the number of handguns sold within the city limits. How would you classify the strength of the relationship?

Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y= -71.12x + 92.48 and the r= -0.571

Recently there has been a rise in fatal accidents caused by “distracted driving.” The United States National Highway Traffic Safety Administration (NHSTA) defines a distraction as anything that diverts attention from driving. The following model estimates the trend in distracted driving accidents over time based on data from the NHSTA:D = 0.015t - 29.97 In this model, D is the decimal to be turned into a percentage of all fatal accidents caused by distracted driving, and t is any calendar year between 2000 and 2020. Use the model to estimate the rate for 2005 and 2020. Note: this means to plug n 2005 for t and simplify and then turn your answer into a percent.  Then plug in 2020 for t and simplify and then turn your answer into a percent.

Write down the properties of R2 . If R2=35.7%, interpret your data. Distinguish between the correlation and regression with example.

your car is more crowded than you think.  table 5.8 reports results from a 1969 personal transportation survey on "home-to-work" trips in metropolitan areas. The survey stated that the average car occupancy was 1.4 people. check that calculation.