The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student’s grade point average (GPA) at the end of the freshman year (Y) can be predicted from the ACT test score (X). So the director would like to fit a simple linear regression on Y and X.Based on the summary statistics below, please calculate the estimate of .=2666=2385.328=368.886=1183.379 = 93.928

52. Analyzing College Grade Point Average. Recall that in exercise 49 , the admissions officer for Clearwater College developed the following estimated regression equation relating final college GPA to the student's SAT mathematics score and high-school GPA. \[ \hat{y}=-1.41+0.0235 x_{1}+0.00486 x_{2} \] where \[ \begin{aligned} x_{1} & =\text { high-school GPA } \\ x_{2} & =\text { SAT mathematics score } \\ y & =\text { final college GPA } \end{aligned} \] A portion of the associated computer output follows. LO 4, 5, 6

A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 72.Homework Grade (x) Test Grade (y)6565 52527878 82827171 70707676 73738484 84845656 45456868 60607272 57577878 7777Copy Values for CalculatorOpen Statistics CalculatorAnswerAttempt 1 out of 2Regression Equation: Final Answer:

A statistic professor is investigating the relationship between tutorial class size and academic performance for a post-graduate statistics for business and economics course. She collects data on the tutorial class size (number of students) and average class mark (out of 100) for a sample of 15 tutorial classes. Tutorial size (X) 15 25 22 12 28 22 17 29 8 15 22 19 21 27 15 Average mark (Y) 78 67 69 79 58 65 72 61 82 73 68 70 70 65 77 Note: you can use Excel to run a regression. Insert the above data in Excel and then click on Data/Data Analysis/Regression (a) Assuming a linear relationship between X and Y, the professor used the least-squares method and found that the Y intercept (b0) = 91.1918 and the slope (b1) = -1.0568. Interpret the meaning of the slope. Answer: for each additional student in a tutorial class, the average (tutorial) class mark is estimated to decrease by around 1.06 points, on average. Note: the word “average” is written twice because the unit of measurement of the dependent variable (Y) is average mark. The slope coefficient indicates the average change in Y associated with a one-unit change in X. (b) Predict the mean value of Y for X = 16, and interpret it

Find the regression line associated with the set of points. (Round all coefficients to four decimal places.)(5, 7), (7, 11), (11, 15), (13, 3)y(x) = −0.1786x+9.9643 Graph the data and the best-fit line. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)

The following data is used to apply a linear regression algorithm with leastsquares regression line Y=a1X. Then, the approximate value of a1 is given by:(X-Independent variable, Y-Dependent variable)X 1 20 30 40Y 1 400 800 1300a. 27.876b. 32.650c. 40.541d. 28.956