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Linear Regression and Chi-Square Hypothesis Test

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Choose any two sets of data. Perform linear regression and hypothesis test on the data. Interpret the results.

[please refer to the attachment for details]

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Solution Preview

Please refer to the attachments for the solutions.

AIM:
My aim is to find out if there exists a linear correlation between 'Sleep Deprivation' and 'Exam Grade'.
A survey was conducted between 12 students on how many hours they slept before a particular exam and their respective grades scored in that exam. Many students had stayed up late several nights before the exam in order to 'cram' for the exam. The average hours of sleep per student were noted and a 'sleep deprivation' index was calculated for each student and plotted against their exam grade:

Student SET 1
(X)
Sleep Deprivation SET 2
(Y)
(XY)
X^2
1
2
3
4
5
6
7
8
9
10
11
12
2
3
3
5
9
12
13
14
15
15
19
20 74
85
87
80
76
71
70
71
68
60
65
52 148
255
267
400
684
852
910
994
1020
900
1235
1040 4
9
9
25
81
144
169
196
225
225
361
400
∑ 130 859 8705 1848
x ̅ 10.83 71.58

PRESENTING:
[Please refer to the attachment 'Solution.xlsx', Sheet 1]
ANALYSIS:
[Please refer to the attachment 'Solution.xlsx', Regression Analysis]
On the x-axis, the known or the independent variable (Sleep Deprivation) is plotted and along the y axis the unknown or the dependent variable (Exam Grade) is plotted.

In regression analysis, if all the points lie exactly on the regression line, then we get a correlation ...

Solution Summary

The solution provides step-by-step method of performing regression analysis and chi-square hypothesis test. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained in details. Regression Analysis has been performed in EXCEL.

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