This report will focus on the data below, which evaluates the relationship of weight and MPG for cars.
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.
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.
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
Analysis of variance table for regression model:
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.
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.