Question

Came across the following question in a past examination paper. And i keep getting wrong each time I attempt it.  $Screenshot_20210902-104051.png$

Having successfully completed your first year in university, you began your second year with an evaluation of your past performance. You observed that you performed well in those subjects where you were diligent with class attendance whilst you performed poorly in those courses where you missed a number of classes. Upon learning about OLS regression you realize that you are able to predict your average performance based on the number of classes attended. The table below shows your data set.

Number of Lectures (X)	Percentage Scored (Y)
1	30
2	45
3	51
4	57
5	60
6	65
7	70
8	71
9	72
10	73
11	66
12	71
13	47
14	81
15	83
16	84
17	89
18	99
19	82
20	86

(i) Compute the following \(x, y, x y, y^{2}, x^{2}, X Y, Y^{2}\) and \(X^{2}\) and your regression intercept and slope.

(ii) Compute your \(Y_{i}\) and plot your Sample regression line.

(iii) Construct a 95% confidence interval for your slope and intercept.

(iv) Assuming the \(r^{2}\) for this regression is 0.89 what is the interpretation of this. Why is it not 100% [give an example in your explanation].

(v) Conduct a test to determine if the additional variable improves overall significance at 10% level of significance.