Chapter 12: Linear Regression Concepts Jonathan Hill Question 1 Do/1 pt ( 3 99 If the correlation coefficient is negative, this means O there is no correlation between the variables the test statistic, t, can not be calculated O the slope of the regression line is negative O the regression line can be used for prediction the calculation was done wrong O there is a strong correlation between the variables Hint: Help Question Help: ) Message instructor Question 2 Go/ pt (3 097 If the correlation coefficient is negative, this means O the test statistic, t, can not be calculated the calculation was done wrong O the slope of the regression line is negative there is no correlation between the variables there is a strong correlation between the variables O the regression line can be used for prediction Question Help: () Message instructor Question 3 Corpt ( 3 99A researcher wishes to examine the relationship between years of schooling completed and the number Sally decides to make and sell necklaces to earn money to buy a new computer. She plans to charge $ of pregnancies in young women. Her research discovers a linear relationship, and the least squares line 5.00 per necklace. The function R(n) = 5.00n describes the revenue, R(n), she will make by is: y = 2 - 5x where x is the number of years of schooling completed and y is the number of selling what is the y-intercept of this function, and what does it mean? pregnancies. The slope of the regression line can be interpreted in the following way: when amount of schooling increases by one year, the number of pregnancies tends to decrease by $5.00, which means that when Sally sells 0 necklaces, she has made $5.00 $5.00, which means she makes $5.00 on each necklace. When amount of schooling increases by one year, the number of pregnancies tends to increase by $0, which means that when sally has sold ( necklaces, she has made $0. $0, which means she makes $0 on each necklace. when amount of schooling increases by one year, the number of pregnancies tends to increase by when amount of schooling increases by one year, the number of pregnancies tends to decrease by Question Help: Message instructor . Question 6 Go/1 pt ( 3 99 Question Help: ) Message instructor Question 0/1 pt () 3 99 If the equation of the regression line that relates income in dollars of student's parents, x , with cost in y, isy = 8000 + 0.02x , then the slope tells us that for every dollar increase in tuition, student's parent's income tends to be 2 cents higher. false true Hint: Help Question Help: ) Message instructor Question 5 Go/1 pt ( 3 99 From 1985 to 2003, the number 3 of federally insured banks could be approximated by B(t) = - 323.4t + 13794 where t is the year and t=0 corresponds to 1985. The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. How many federally insured banks were there in 1990? Year Retail Sales 85.851 3 108.426 Find the slope of the graph of B- 41.781 169.256 interpret this slope as a rate of change. Choose the correct answer below. 202.297 The number of banks decreased by 323.4 banks per 222.266 The number of banks increased by 12177 banks per year OThe number of banks increased by 323.4 banks per year Let y be the retails sales in billions of dollars in z years since 1995. A linear model for the data is y = 9.44x + 84.182. The number of banks decreased by 12177 banks per y The number of banks decreased by 13794 banks per year The number of banks increased by 13794 banks per year Find the y-intercept of the graph of B. The y-intercept is Interpret the y-intercept. Choose the correct answer below. The y-intercep er of banks in 1985 The y-intercept is the number of banks in 2003 The y-intercept is the n mber of banks in 1990 The y-intercept is the minin number of banks allowed in the country The y-intercept is the maximum number of banks allowed in the country A) Use the above scatter plot to decide whether the line of best fit, fits the data well. Question Help: Message instructor The function is not a good model for the data Question 7 (o/1 pt () 3 95 The function is a good model for the data. B) To the nearest billion, estimate the retails sales in the U. S. in 2017. billions of dollars. () use the equation to find the year in which retails sales will be $239 billion. Question Help: Message instructor . Question 8 0/1 pt 9 3 0 99The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. Year Retail Sales 2 11.7 8.6 6.8 3.3 2.4 2.6 2.7 0.5 0 85.85 y 13.9 11.1 9.7 6.6 5.8 6 6 4.2 3 103.426 x = thousands of automatic weapons 6 141.781 y = murders per 100,000 residents 9 169.256 12 202.297 This data can be modeled by the equationy = 0.872 + 3.73. Use this equation to answer the 15 following; 222.266 A) How many murders per 100,000 residents can be expected in a state with 7.2 thousand automatic weapons? Let S( t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t) = 9.44t + 84.182. Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 10.9 thousand automatic weapons? Answer = Round to 3 decimal places. Question Help: ) Video () Message instructor 150- Question 10 Co/1 pt ( 3 99 140- 130- The table below shows the number of state-registered automatic weapons and the murder rate for 120- several Northwestern states. 211.7 8.6 6.6 3.6 2.3 2.3 2.7 0.3 root y 14.1 11.5 9.6 7.1 6.3 6.2 6 4.1 90- x = thousands of automatic weapons 804 y = murders per 100,000 residents Use the above scatter plot to decide whether the linear model fits the data well. This data can be modeled by the equationy = 0.87x + 3.99. Use this equation to answer the O The function is a good model for the data. following; The function is not a good model for the data A) How many murders per 100,000 residents can be expected in a state with 9 thousand automatic weapons? Estimate the retails sales in the U. S. in 2015. billions of dollars. Use the model to predict the year in which retails sales will be $230 billion. Answer = Round to 3 decimal places. Question Help: [) Message instructor B) How many murders per 100,000 residents can be expected in a state with 6.4 thousand automatic weapons? Question 9 ( o/1 pt ( 3 99 Answer = Round to 3 decimal places. Question Help: ) Message instructor