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

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

he marks obtained by 40 students out of 50 in a class are given below in the table.Marks (in $)4236304550Number of Students7101382Find the mode of the above data.

(1 point) Suppose there are three sections of a Statistics course taught by the same instructor. The class averages for each section on Test 1 are displayed in the table below.Class Size Class AverageSection 01 22 77Section 02 27 76Section 03 16 85

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

Consider the following data:               12 students get less than 10 marks   18 students get less than 20 marks  30 students get less than 30 marks  40 students get less than 40 marks  56 students get less than 50 marksHow many students get marks between 30-40 marksSelect one:a.70b.30c.40d.10