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Created: Mar 10, 2010
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StatsCrunch Assignment #2 - Eapen

This report will focus on the data below, which evaluates the relationship of weight and MPG for cars.

Data set 1. Weight and MPG of Cars   [Info]

Scatter Plot – Weight & MPG  Based on the scatter diagram, the relationship between these two variables  are of negative association as indicated by the linear patter of negative slopes.

Result 1: Scatter Plot MPG   [Info]

Simple Linear Regression  When the value of weight is at 2.0, the predicted value of the MPG is 32.07.  Slope is -8.367 which is same as the Beta.

Correlation – Weight & MPG  To determine if there is a linear relation between the weight and MPG, we will compare the critical value and the correlation of the data sets. The data set has 37 observations, therefore the critical value is 0.325.  The correlation of the 2 data sets is -0.905.  The correlation is smaller than the critical value; therefore,  we can conclude there is a negative linear relation exist between weight and MPG.

Result 2: Simple Linear Regression   [Info]
Simple linear regression results:
Dependent Variable: MPG
Independent Variable: Weight
MPG = 48.8024 - 8.367461 Weight
Sample size: 37
R (correlation coefficient) = -0.9054
R-sq = 0.8196811
Estimate of error standard deviation: 2.7817576

Parameter estimates:
 Parameter Estimate Std. Err. DF T-Stat P-Value Intercept 48.8024 1.9698044 35 24.775251 <0.0001 Slope -8.367461 0.66337305 35 -12.613508 <0.0001

Analysis of variance table for regression model:
 Source DF SS MS F-stat P-value Model 1 1231.1482 1231.1482 159.10059 <0.0001 Error 35 270.83612 7.738175 Total 36 1501.9844

Predicted values:
 X value Pred. Y s.e.(Pred. y) 95% C.I. 95% P.I. 2 32.067474 0.7458818 (30.553255, 33.581696) (26.220724, 37.914227)

Simple Linear Regression MPG  I searched for a pattern in the data, and the graph did not indicate any patterns.  The graph also shows a few outliners.  To verify if there are outliers, I created a Boxplot and Boxplot indicated no outliers.

Result 3: Simple Linear Regression MPG   [Info]

Boxplot  There are no outliers showing in the Boxplot.  The median is in the center of the box which indicates the residuals are symmetric.  Left tail is longer than the right tail, therefore, the graph is skewed to the left.

Result 4: Boxplot MGP   [Info]