Question

Yield	Constant	Time	Method
54.6	1	16	0
45.8	1	10	0
57.4	1	11	0
40.1	1	2	0
56.3	1	20	0
51.5	1	18	0
50.7	1	9	0
64.5	1	15	0
52.6	1	1	0
48.6	1	5	0
74.9	1	12	1
78.3	1	19	1
80.4	1	14	1
58.7	1	6	1
68.1	1	8	1
64.7	1	3	1
66.5	1	7	1
73.5	1	4	1
81	1	17	1
73.7	1	13	1

1. Regress Yield = f(Method)

2. Sort the Data. Redo 1. Compare results.

3. Regress Yield = f(Method, Time) What is your understanding of time? Compare results with 1 and 2.

4. Regress Time = f(Method) What does this model measure?

Answer 1

Q1. Regress Yield = f(Method)

Regression Statistics
Multiple R	0.82970177
R Square	0.688405027
Adjusted R Square	0.671094196
Standard Error	7.010171182
Observations	20
Residual Output
Observation	Predicted Y	Residuals
1	52.21	2.39
2	52.21	-6.41
3	52.21	5.19
4	52.21	-12.11
5	52.21	4.09
6	52.21	-0.71
7	52.21	-1.51
8	52.21	12.29
9	52.21	0.39
10	52.21	-3.61
11	71.98	2.92
12	71.98	6.32
13	71.98	8.42
14	71.98	-13.28
15	71.98	-3.88
16	71.98	-7.28
17	71.98	-5.48
18	71.98	1.52
19	71.98	9.02
20	71.98	1.72

Regression of Yield using Method has a R-Square value of .688, which means 68.8% of the variance of Yield is explained by Method itself.

While analyzing the residuals, it can be observed that the predicted Yield has only 2 kinds of values: - 52.21 and 71.98 and this depends on the type of method selected (0 or 1). Since method is acting as a binary variable here, so the predicted value of yield is also limited to 2 states only.

Q2. Sort the Data. Redo 1. Compare results

Regression Statistics
Multiple R	0.82970177
R Square	0.688405027
Adjusted R Square	0.671094196
Standard Error	7.010171182
Observations	20
Residual Output
Observation	Predicted Y	Residuals
1	52.21	2.39
2	52.21	-6.41
3	52.21	5.19
4	52.21	-12.11
5	52.21	4.09
6	52.21	-0.71
7	52.21	-1.51
8	52.21	12.29
9	52.21	0.39
10	52.21	-3.61
11	71.98	2.92
12	71.98	6.32
13	71.98	8.42
14	71.98	-13.28
15	71.98	-3.88
16	71.98	-7.28
17	71.98	-5.48
18	71.98	1.52
19	71.98	9.02
20	71.98	1.72

Sorting the values do not affect the regression model as regression don’t depend on the order of the input data, rather it depends only on the values of the input variable (independent variable) and its effect on the output variable (dependent variable)

Q3. Regress Yield = f(Method, Time) What is your understanding of time? Compare results with 1 and 2.

Regression Statistics
Multiple R	0.909929
R Square	0.827971
Adjusted R Square	0.807732
Standard Error	5.359768
Observations	20
Residual Output
Observation	Predicted Y	Residuals
1	45.49062	-5.39062
2	51.66936	-5.86936
3	47.80765	0.792353
4	50.89702	-0.19702
5	57.8481	-6.3481
6	44.71828	7.881724
7	56.30342	-1.70342
8	59.39279	-3.09279
9	52.4417	4.958297
10	68.65893	-9.95893
11	55.53107	8.968927
12	66.3419	-1.6419
13	69.43127	-2.93127
14	70.20361	-2.10361
15	67.11424	6.385759
16	74.06533	-0.36533
17	73.29298	1.607017
18	78.69938	-0.39938
19	74.83767	5.562332
20	77.1547	3.845304

When we regressed Yield with both method and time, the R-square value jumped to .827, i.e., now 82.7% of the variation in the model can be explained by the 2 independent variables (Method and Time).

Analyzing the residuals also suggests that predicted Yield values are dynamic and since it depends on one binary variable (Method) and a continuous variables (Time), the Yield values are continuous in nature

Time is basically the length of period for which a person remains invested and it is visible that with the increase in time, Yield increases accordingly.

Q4. Regress Time = f(Method) What does this model measure?

Regression Statistics
Multiple R	0.034684
R Square	0.001203
Adjusted R Square	-0.05429
Standard Error	6.074537
Observations	20
Residual Output
Observation	Predicted Y	Residuals
1	10.7	-8.7
2	10.7	-0.7
3	10.7	-5.7
4	10.7	-1.7
5	10.7	7.3
6	10.7	-9.7
7	10.7	5.3
8	10.7	9.3
9	10.7	0.3
10	10.3	-4.3
11	10.7	4.3
12	10.3	-7.3
13	10.3	-3.3
14	10.3	-2.3
15	10.3	-6.3
16	10.3	2.7
17	10.3	1.7
18	10.3	8.7
19	10.3	3.7
20	10.3	6.7

Regressing time and method is not giving a very insightful or useful model. With a meagre R-squared value of .0012, it is basically calculating the average of the independent variable (method) to predict the dependent variable (time). The penalty of regressing these 2 variables is actually pulling the adjusted R-Square to negative.