Question

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!

Answer 1