You are considering developing a truancy reduction intervention, but first, you are interested in confirming that the total number of days students are absent from high school actually correlates with their grade point averages (GPAs). You obtain school records that list the total absences and GPAs for 400 graduating fourth-year students. You calculate the Pearson correlation coefficient, r = 0.81, and find a strong linear relationship. However, for the regional government to consider doing anything about this issue, it wants proof that at least 50% of variability in GPA can be explained by the relationship between the GPA and the total number of absences. Luckily, you can use r to calculate the coefficient of determination to determine the percentage variation explained by the relationship. What is the relationship between the coefficient of determination and the proportion of variation explained by the relationship between two variabilities? The coefficient of determination is the square of the proportion of variation explained by the relationship between two variabilities. The coefficient of determination is the proportion of variation explained by the relationship between two variabilities. The coefficient of determination is the proportion of variation not explained by the relationship between two variabilities. O The square of the coefficient of determination is the proportion of variation explained by the relationship between two variabilities. The coefficient of determination for the relationship between the GPA and the total number of absences is What is the percentage of variation explained by this relationship? 0.04 0.66 O 34% 0.81 O 96% 0.10 O 4% 66% This relationship strong enough that the regional government should consider doing something about this issue. What is the percentage of unexplained variation? 66% 34% O 4% 96%Suppose you are trying to understand why' universityf students gamble {number of times each month that a student gambles}. You examine factors such as disposable income {in units of $100}, credit card debt, illicit drug use, and parental problems with gambling. Parental Gambling (1!) Student Gambling Frequency (Y) 2 2 3 3 4 4 1 6 10 10 ThemeanXscoreisf=| 4|,and the meaancoreisl7=| 5|. Now, using the values for the means that you just calculated, ll out the following table by calculating the deviations from the means for X and Y, the squares of the deviations, and the products of the deviations. (Note: Use a minus sign [-} to enter a negative value.) Table: Parental Gambling and Student Gambling Frequencvr Calculations Scores Deviations Squared Deviations Product: X y XX YP (Jrff (YJ')2 (xJ'r)(yY) 2 2 | -2| | -3| | 4| | 9| | 6| 3 3 | -1| | -2| | 1| | 4| | 2| 4 4 | 0| | -1| | 0| | 1| | 0| 1 6 | -3| | 1| | 9| | 1| | -3| 10 10 | 6| | 5| | 35| | 25| | sol The covariation between the number of times each month that the parent gambles and the number of times each month that the student gambles i535v According to your calculations in the table, the correlation coefficient [otherwise known as Pearson's r} describing the relationship between the number of times each month that the parent gambles and the number of times each month that the student gambles is 0.?8 V . Which of the following accuratelv describes the relationship between the number of times each month that the parent gambles and the number of times each month that the student gambles? O No linear relationship 0 A perfect linear relationship 0 A strong negative linear relationship 0 A strong positive linear relationship 0n the basis of these results, would you endorse an intervention that was thoughtful, effective, and targeted students with parents who gambled? 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 4 3 Matt 2 3" Nikki 1 5 Tyler 3 8 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 Yintercept. The rst step in calculating these values is to calculate the means of X and Y. The mean X score is? = 2.5 , and the mean Y score is f = 10 . 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 17 [X Y) (Y - 17) {X - if Tina 4 E 8 1 1.5 v 2.25 v Matt 2 -0.5 v 7 u g 0.25 v Nikki 1 -1.5 v s -2 1 2.25 v Tyler 3 g 3 1_ 0.5 v 0.25 v To calculate the slope and the Yintercept, you first will have to calculate the covariation of X and Y, z. {X X} (Y Y), and the sum of the squared deviations around the mean of X, ELY if. Luckily. you have already done most of the work. The covariation ofX and Y is 5.00 V , and the sum of the squared deviations around the mean of)