Data needs to be analyzed
For this assignment I have to analyze the regression (relationship between 2 independent variables and 1 dependent variable). Below is all of my data and values. I need help answering the questions that are at the bottom. Questions regarding the strength of the relationship
Sum of X1 = 184.6
Sum of X2 = 21307.03
Sum of Y = 2569.1
Mean X1 = 3.6196
Mean X2 = 417.7849
Mean Y = 50.3745
Sum of squares (SSX1) = 33.8204
Sum of squares (SSX2) = 14931428.3367
Sum of products (SPX1Y) = 71.8455
Sum of products (SPX2Y) = 54585.5864
Sum of products (SPX1X2) = 1642.7001
Regression Equation = ŷ = b1X1 + b2X2 + a
b1 = ((SPX1Y)*(SSX2)-(SPX1X2)*(SPX2Y)) / ((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2)) = 983088040.09/502288298.2 = 1.95722
b2 = ((SPX2Y)*(SSX1)-(SPX1X2)*(SPX1Y)) / ((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2)) = 1728085.34/502288298.2 = 0.00344
a = MY - b1MX1 - b2MX2 = 50.37 - (1.96*3.62) - (0*417.78) = 41.85279
ŷ = 1.95722X1 + 0.00344X2 + 41.85279
Sum of X1 = 184.6
Sum of X2 = 21307.03
Sum of Y = 2569.1
Mean X1 = 3.6196
Mean X2 = 417.7849
Mean Y = 50.3745
Sum of squares (SSX1) = 33.8204
Sum of squares (SSX2) = 14931428.3367
Sum of products (SPX1Y) = 71.8455
Sum of products (SPX2Y) = 54585.5864
Sum of products (SPX1X2) = 1642.7001
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Model: y = 41.8528 + 1.9572 * x1 + 0.0034 * x2
Predictor |
Coefficient |
Estimate |
Standard Error |
t-statistic |
p-value |
Constant |
B0 |
41.8528 |
4.9857 |
8.3946 |
0 |
x1 |
B1 |
1.9572 |
1.3409 |
1.4596 |
0.1509 |
x2 |
B2 |
0.0034 |
0.002 |
1.7048 |
0.0947 |
R-Squared |
R2 = 0.1016 |
Adjusted R-Squared |
R2 adj = 0.0642 |
Residual Standard Error |
7.7775 on 48 degrees of freedom |
Overall F-statistic |
.7147 on 2 and 48 degrees of freedom |
Overall p-value |
0.0764 |
Analysis of Variance Table
Source |
df |
SS |
MS |
F-statistic |
p-value |
Regression |
2 |
328.415 |
164.2075 |
2.7147 |
0.0764 |
Residual Error |
48 |
2903.4619 |
60.4888 |
||
E=Total |
50 |
3231.8769 |
64.6375 |
1. Find the model with the most explanatory power and significant estimates. Describe what your regression output shows regarding the statistical properties of your model.
2. What does this model suggest regarding the relationships between your variables?
3. Do you think your data more or less satisfy OLS regression assumptions? Explain why? Or why not?
4. Based on 3), do you think your analysis is reliable?
There are 3 variables (2 independent variables and 1 dependent variable). I need help analyzing my data and answering these questions regarding the regression (relationship between all variables). Thank you!
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