Math Problem Solver

1. The information on average attendance and grade achieved (both in %) in a core

module for a random sample of 7 first year students is provided below.

Student Attendance Grade

1 84 64

2 85 58

3 78 56

4 90 68

5 91 68

6 61 54

7 59 40

(a) Calculate the least squares regression line Y = βˆ

0 + βˆ

1X with the formulae

method, using attendance as the independent variable and grade as the dependent

variable (round the parameter estimates to 2 decimal places). Interpret your

answer. [5]

(b) Calculate and interpret the value of the sample correlation coefficient r. Carry

out a t-test for the null hypothesis that the true value of the correlation coefficient

is equal to zero, and explain your answer. Report the value of the correlation

coefficient and test statistic, rounded to 2 decimal places. [4]

(c) Given your estimate, work out the attendance rate (rounded to 2 decimal places)

below which one would expect students to achieve grades lower than 40% and

fail the module. How reliable do you think this prediction is and why?