Regression analysis can be used to analyze how a change in one variable impacts
ID: 3040745 • Letter: R
Question
Regression analysis can be used to analyze how a change in one variable impacts the other variable, such as an increase in a marketing budget increasing sales. Find a unique area of your life where one variable impacts the other variable (being sure that are both measurable) and do a regression analysis on it. Remember to include the coefficient of determination as well as the test of significance. Share your results and make any comments as to whether or not there is a possibility of potential problems (causation or extrapolation) with your results. (please type answer)
Explanation / Answer
Solution:
Regression analysis is very useful in many real time life applications. In my educational curriculum, I observed that the amount of time that spent (private time) preparing for exam and the score that I obtained in the exam are related.
The variable time spent preparing for exam is measured on continuous scale and the scores obtained exam is also a continuous type.
The average time spent before taking the exam is the independent variable. The more time you spend you obtain results with more marks and the less time spent results in less marks.
So the time spent is a definite causation to get good marks/score.
The average private time per day that I spent before taking the exam and the score that I obtained in that examination for past 10 tests were noted down.
Since the maximum scores are different in each test and for each subject, the marks adjusted in each test is averaged to 100. i.e The number of marks/100
Test No:
Time spent (hrs)
Scores obtained
1
2
75
2
1.75
70
3
2.5
78
4
3
80
5
1.5
68
6
1
65
7
2.75
76
8
3
76
9
3.5
80
10
3.25
81
The Regression analysis using Excel Data Analysis option, and below is Regression output.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.94283319
R Square
0.88893442
Adjusted R Square
0.87505122
Standard Error
1.93931901
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
240.8123
240.8123
64.02952
4.35958E-05
Residual
8
30.08767
3.760958
Total
9
270.9
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
59.7023445
1.995825
29.91361
1.69E-09
55.09996315
64.30472594
Time spent (hrs)
6.26707441
0.783204
8.001845
4.36E-05
4.4610034
8.073145428
The regression line is Scores obtained (Y) = 59.70 + 6.267 * Time spent
The slope of the regression line is 6.267 . This means for every unit (one hour) increase in time spent there is a 6.267 times increase in the score.
The P-value corresponding to Time spent ( independent variable) is less than 0.005 signifies the relationship is significant.
The R-Square value is 0.8889. This means 88.89% of the variation in the variable scores obtained is explained by the independent variable.
Test No:
Time spent (hrs)
Scores obtained
1
2
75
2
1.75
70
3
2.5
78
4
3
80
5
1.5
68
6
1
65
7
2.75
76
8
3
76
9
3.5
80
10
3.25
81