1. Using the regression line to make predictions about Y Suppose you are interested in the relationship between foster care and incarceration for young adults who have been involved in the juvenile justice system. You are able to access some anonymous data from 75 30-year-old graduates of the juvenile justice system. The following table shows the data from four of these graduates from your sample. Their results are typical of the rest of your sample. You would like to use the number of foster placements to make predictions about the number of arrests. Table: Number of Foster Placements and Number of Arrests Graduate Foster Placements Arrests Tina 7 Matt 2 Nikki Tyler un You can use the preceding sample data to obtain the least-squares regression line: Y = a+bX To be able to use this line to predict Y values based on a known value of X, you will first have to calculate the slope and the Y-intercept. The first step in calculating these values is to calculate the means of X and Y. The mean X score is X = 2.5 , and the mean Y score is Y = 5.0 . Now you are ready to complete the following computation table: Table: Computations for Number of Foster Placements and Number of Arrests Graduate Foster Placements X -X Arrests Y - Y (X - X) ( Y- Y) (X - X)? Tina 1.5 7 2 3 2.25 Matt N -0.5 4 0.5 0.25 7 Nikki -1.5 1.5 2.25You can use the preceding sample data to obtain the least-squares regression line: Y = a + bx To be able to use this line to predict Y values based on a known value of X, you will rst have to calculate the slope and the Yintercept. The rst step in calculating these values is to calculate the means of X and Y. Now you are ready to complete the following computation table: The mean X score is i = .. and the mean Y score is ? = Table: Compuiations for Number of Foster Placements and Number of Arrests Graduate Foster Placements X i Arresls Y Y (X i] (Y ?) (X i]2 Tina 4 1.5 Y 7 2 Y 3 V 2.25 Y Matt 2 41.5 V 4 -l V 0.5 V 0.25 7 Nikki 1 -1.5 Y 4 -1 Y 1.5 V 2.25 Y Tyler 3 0.5 v 5 I] v o v 0.25 v To calculate the slope and the Yinteroept, you rst will have to calculate the oovariation of X and Y, 2(1 i) (Y ?), and the sum of the squared deviations around the mean of K, XXX if. Luckily, you have already done most of the work. The covariation of X and Y is Y , and the sum ofthe squared deviations around the mean ofX is Y . Now you can calculate the slope and the Yinteroept. The slope of the leastsquares regression line is Y . The Yintercept of the least-squares regression line is Y . You now have everything you need to use the leastsquares regression line to estimate the number of arrests for someone who had ve foster placements. The leastsquares regression line suggests that a 30yearold graduate of the juvenilejustice system who had ve foster placements would have V arrests. What might the implications of this research nding be on policy? To be able to use this line to predict Y values based on a known value of X, you will rst have to calculate the slope and the Yintercept. The rst step in calculating these values is to calculate the means of X and Y. The mean X score is X - Now you are ready to complete the following computation table: ,. and the meanNr score is ? = Table: Computations for Number of Foster Placements and Number of Arrests Graduate Foster Placements X i Arrests Y Y (X i] (Y ?:I (X i]; Tina 4 1.5 Y .7 2 Y 3 V 2.25 Y Matt 2 -'l].5 Y 4 -l V 0.5 V 0.25 Y Nikki 1 -1.5 Y 4 -l V 1.5 V 2.25 Y Tyler 3 0.5 v 5 Ill 7 0 v 0.25 v To calculate the slope and the Yintercept, you rst will have to calculate the covariation of X and Y, E (X i] (Y ?), and the sum of the squared deviations around the mean of X, XXX if. Luckily, you have already done most of the work. The coyariation of X and Y is Y , and the sum ofthe squared deviations around the mean ofX is Y . Now you can calculate the Si e Yinteroept. The slope of the leastsquare an line is Y . The Yintercept of the leastsquares regression line is Y . You now have everything you need to use the leastsquares regression line to estimate the number of arrests for someone who had Five foster placements. The leastsquares regression line suggests that a Bilyea rolcl gladuate of the juvenilejustice system who had ve foster placements would have V arrests. What might the implications of this research nding be on policy? You can use the preceding sample data to obtain the least-squares regression line: Y = a + bx To be able to use this line to predict Y values based on a known value of X, you will rst have to calculate the slope and the Yintercept. The rst step in calculating these values is to calculate the means of X and Y. The mean X score is i = .. and the mean Y score is ? = Now you are ready to complete the following computation table: Table: Computations for Number of Foster Placements and Number of Arrests Graduate Foster Placements X i Arrests Y Y (X i] (Y ?) (X if Tina 4 1.5 Y 7 2 Y 3 V 2.25 Y Matt 2 41.5 Y 4 -1 Y 0.5 V 0.25 Y Nikki 1 -1.5 Y 4 -1 Y 1.5 V 2.25 Y Tyler 3 0.5 Y 5 n Y 0 V 0.25 Y To calculate the slope and the Yintercept, you rst will have to calculate the covariation of X and Y, E (X i] (Y ?), and the sum of the squared deviations around the mean of X, XXX XYi. Luckily, you have alreadyr done most of the work. The covariation of X and Y is Y , and the sum ofthe squared deviations around the mean ofX is Now you can calculate the slope and the Yintercept. The slope of the leastsquares regression line is Y . The Yintercept of the leastsquares regression line is Y . You now have everything you need to use the leastsquares regression line to estimate the number oi arrests for someone who had ve foster placements. The leastsquares regression line suggests that a 30year-old graduate of the juvenllejustice system who had ve foster placements would have V arrests. What might the implications of this research nding be on policy? You can use the preceding sample data to obtain the least-squares regression line: Y = a + bX To be able to use this line to predict Y values based on a known value of X, you will first have to calculate the slope and the Y-intercept. The first step in calculating these values is to calculate the means of X and Y. The mean X score is X = 2.5 , and the mean Y score is Y = 5.0 Now you are ready to complete the following computation table: Table: Computations for Number of Foster Placements and Number of Arrests Graduate Foster Placements X -X Arrests Y - Y ( X - X ) ( Y - Y) X - X)? Tina 1.5 2 3 2.25 Matt -0.5 -1 0.5 0.25 Nikki -1.5 1.5 2.25 Tyler W 0.5 5 0.25 To calculate the slope and the Y-intercept, you first will have to calculate the covariation of X and Y, _ (X - X) (Y - Y), and the sum of the squared deviations around the mean of X, _(X - X) . Luckily, you have already done most of the work. The covariation of X and Y is , and the sum of the squared deviations around the mean of X is Now you can calculate the slope and the Y-intercept. The slope of the least-squares regression line is The Y-intercept of the least-squares regression li -2.00 1.00 You now have everything you need to use the le es regression line to estimate the number of arrests for someone who had five foster 2.00 placements. The least-squares regression line su hat a 30-year-old graduate of the juvenile justice system who had five foster placements would have arrests. -1.00 What might the implications of this research finding be on policy?You can use the preceding sample data to obtain the least-squares regression line: Y = a + bX To be able to use this line to predict Y values based on a known value of X, you will first have to calculate the slope and the Y-intercept. The first step in calculating these values is to calculate the means of X and Y. The mean X score is X = 2.5 , and the mean Y score is Y = 5.0 Now you are ready to complete the following computation table: Table: Computations for Number of Foster Placements and Number of Arrests Graduate Foster Placements X-X Arrests Y- Y ( X - X ) ( Y - Y) ( X - X )= Tina 1.5 3 2.25 Matt 0.5 0.5 0.25 Nikki -1.5 4 1.5 2.25 Tyler 0.5 To calculate the slope and the Y-intercept, you first will have to calculate the covariation of X and Y, _ (X - X) (Y - Y), and the sum of the squared deviations around the mean of X, _(X - X)". Luckily, you have already done most of the work. The covariation of X and Y is , and the sum of the squared deviations around the mean of X is Now you can calculate the slope and the Y-intercept. The slope of the least-squares regression line is The Y-intercept of the least-squares regression line is You now have everything you need to use the least-so 5.50 egression line to estimate the number of arrests for someone who had five foster placements. The least-squares regression line suggest 2.50 30-year-old graduate of the juvenile justice system who had five foster placements would have V arrests. 7.50 What might the implications of this research finding b|4.50 icy?You can use the preceding sample data to obtain the least-squares regression line: Y=a+bX To be able to use this line to predict Y values based on a known value of X, you will rst have to calculate the slope and the Yinteroept. The rst step in calculating these values is to calculate the means of X and Y. The mean X score is i - , and the mean Y score is ? = Now you are ready to complete the following computation table: Table: Computations for Number of Foster Placements and Number of Arrests Graduate Foster Placements X i Arrests Y Y (X i] (Y ?) (X i]? Tina 4 1.5 Y 7 2 Y 3 V 2.25 Y Matt 2 41.5 Y 4 -1 Y 0.5 V 0.25 Y Nikki 1 -1.5 Y 4 -1 Y 1.5 V 2.25 Y Tyler 3 0.5 Y 5 n Y 0 Y 0.25 Y To calculate the slope and the Yinteroept, you rst will have to calculate the covariation of X and Y, E {X E (Y ?), and the sum of the squared deviations around the mean of X, XXX if. Luckily, you have alreadyr done most of the work. The covariation of X and Y is Y , and the sum ofthe squared deviations around the mean of X is Y . Now you can calculate the slope and the Yinteroept. The slope o tsquares regression line is Y . The Yinter e leastsquares regression line is Y . You now ha hing you need to use the leastsquares regression line to estimate the number of arrests for someone who had ve foster placements stsquares regression line suggests that a 30yearold graduate of the juvenile justice system who had ve foster placements would have V arrests. What might the implications of this research nding be on policy