Your Task is to: Pick two variables, collect data, graph the data, create an est
ID: 3217480 • Letter: Y
Question
Your Task is to: Pick two variables, collect data, graph the data, create an estimated regression equation and analyze by hand and then using Excel to verify your results. Your project should be interesting and meaningful! Do something different than what's in the book or my examples!! Data is provided below the questions.
1.Explain what your project is about.
2.How did you collect your data? Why is it a good representation of the relationship between the two variables?
3.Create a regression equation. Do all your work by hand as illustrated in chapter 14 sections 14.1 through 14.5. See top of this page for ways you can do this.
4.Use Excel to verify your results. Include Excel file showing all your data, graph and regression analysis electronically.
5.What conclusion can you make concerning the relationship between the variables?
6.Were you surprised with the results? Why?
7.Analyze the results. Do the results make sense? Why? Do you suspect any cause/effect issues that may be involved? Explain.
8.Show examples of using your regression equation to calculate and predict values of the dependent variable.
Stolen Recovered JAN 44 37 FEB 22 20 MAR 27 17 APR 28 17 MAY 22 13 JUNE 34 17 JULY 28 17 AUG 28 26 SEPT 41 24Explanation / Answer
1]
The project is about the relationship between the stolen items and recovered items in the specific area.
2]
We collect the data for the two variables such as the number of stolen items and the number of recovered items for the months from January to September. There is a relationship between the number of stolen items and the number of recovered items so it is a good representation of the relationship between two variables.
3]
Here, we have to create the regression equation. The calculation table for the sum of squares and correlation coefficient is given as below:
Stolen X
Recovered Y
X^2
Y^2
XY
44
37
1936
1369
1628
22
20
484
400
440
27
17
729
289
459
28
17
784
289
476
22
13
484
169
286
34
17
1156
289
578
28
17
784
289
476
28
26
784
676
728
41
24
1681
576
984
274
188
8822
4346
6055
X = 274
Y = 188
X^2 = 8822
Y^2 = 4346
XY = 6055
n = 9
Correlation coefficient = r = [nxy - xy]/sqrt[(nx^2 – (x)^2)*(ny^2 – (y)^2)]
Correlation coefficient = r = [9*6055 – 274*188]/sqrt[(9*8822 – 274*274)*(9*4346 – 188*188)]
Correlation coefficient = r = 0.738992783
Sy = standard deviation of y = 7.236097782
Sx = standard deviation of x = 7.74776
b = r*Sy/Sx = 0.738992783*7.236097782/7.74776 = 0.69019
Slope = b = 0.69019
a = ybar – b*xbar
xbar = 30.44444
ybar = 20.88888889
a = 20.88888889 - 0.69019*30.44444
y-intercept = -0.12356
Regression equation is given as below:
Y = a + b*X
Y = -0.12356 + 0.69019*X
Recovered = -0.12356 + 0.69019*Stolen
4]
The regression output by using excel is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.738992783
R Square
0.546110333
Adjusted R Square
0.481268952
Standard Error
5.211653676
Observations
9
ANOVA
df
SS
MS
F
Significance F
Regression
1
228.7595506
228.7595506
8.4222502
0.022916822
Residual
7
190.1293383
27.16133404
Total
8
418.8888889
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-0.12355391
7.445891334
-0.01659357
0.9872239
-17.73028913
17.48318131
Stolen X
0.690189727
0.237823311
2.902111332
0.0229168
0.127826957
1.252552496
From this output, it is observed that the manually calculations for the coefficients and regression equation are approximately correct.
Stolen X
Recovered Y
X^2
Y^2
XY
44
37
1936
1369
1628
22
20
484
400
440
27
17
729
289
459
28
17
784
289
476
22
13
484
169
286
34
17
1156
289
578
28
17
784
289
476
28
26
784
676
728
41
24
1681
576
984
274
188
8822
4346
6055
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