Business Statistics - Week 7 Assignment 1 Week 7 Assignment 1. What is a least squares regression line? What does regression tell us? Answer in at least a paragraph. 2. Given the following from https://fred.stlouisfed.org/series/G160371A027NBEA Government current expenditures: Income security: Welfare and social services Year Billions of Dollars 1960 4.161 1965 5.941 1970 13.335 1975 30.247 1980 48.506 1985 64.651 1990 90.7 1995 129.75 2000 142.631 2005 189.985 2010 262.258 2015 274.928 2018 278.915 2019 289.589 2020 612.259 2021 977.791 a. make a scatter diagram from 1960 to 2015 which shows the trend line (this is the regression line) and provide the coefficient of determination. b. What is the equation of the trend line from the graph? c. What is r here? What is r 2 here ? d. What does r (correlation coefficient) tell us in general? This requires at least a paragraph. Explain what happens if r is negative. e. According to the equation of the trend line from your graph, what would be the expenditure in 2016? Does this value make sense if you compare it to the previous figures in the table? f. According to the equation of the trend line from your graph, if the expenditure was 250 billion dollars, what year would that have been? g. According to the equation of the trend line from your graph, if the expenditure was 300 billion dollars, what year would that have been? Does this value make sense when you compare to the actual amounts in the table?

h. According to the equation of the trend line from your graph, what would be the expenditure in 2021? i. Why is it dangerous to extrapolate outside the experimental region that was from 1960 to 2015? Use the table to answer and see what happens in 2020 and 2021. j. What do you think happened in 2020 and 2021? 3. You are presented with four values for Pearson's product moment correlation coefficient( r). Which one shows the strongest relationship? Why? a. 0 b. 0.19 c. 0.59 d. -0.95