17 Make a scatter plot linked and near the following data:X Y1.01 2.59821.07 2.27521.16 2.5921.19 2.22521.19 3.28431.22 2.191.32 3.61761.38 2.95161.43 3.99711.45 4.08551.46 4.08621.48 4.02721.53 2.84061.56 4.32081.58 3.60521.6 3.591.72 4.87561.75 3.68751.77 4.10421.8 4.5381.81 5.12571.88 4.61921.94 5.49242 5.212.25 -8 18 Make the title Scatterplot of X and Y Data.Add trendline, regression equation, and R2 to the plot. 19 The scatterplot reveals a point outside the point pattern. A “residual” is defined as the veritical distance from the regression line to a data point, or Residual = Observed – Predicted. You can select regression option Residuals to show the residuals. Q1, Q3, and IQR were computed for the residuals. Residuals that are more that 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers and the corresponding data must be investigated. It was determined that the outlying data point was due to data entry error. The data is copied here and outlier removed. Make a new scatterplot linked and near the cleaned data, and add title Scatterplot without Outlier, trendline, and regression equation label. X Y 1.01 2.8482 1.07 2.5252 1.16 2.842 1.19 2.4752 1.19 3.5343 1.22 2.44 1.32 3.8676 1.38 3.2016 1.43 4.2471 1.45 4.3355 1.46 4.3362 1.48 4.2772 1.53 3.0906 1.56 4.5708 1.58 3.8552 1.6 3.84 1.72 5.1256 1.75 3.9375 1.77 4.3542 1.8 4.788 1.81 5.3757 1.88 4.8692 1.94 5.7424 2 5.46 20 Compare the regression results of the two plots. What does the outlier do to the regression line?What does the regression line do when the outlier is removed? Why does R2 increase when an outlier is removed? Share on Facebook Tweet Follow us Sample Answer Analyzing the Impact of Outliers on Regression Analysis Introduction In statistical analysis, outliers can significantly impact the results of regression analysis by skewing the regression line and reducing the accuracy of the model. This essay will explore the effects of outliers on regression analysis using a dataset, demonstrate how outliers affect regression outcomes, and explain the changes observed when outliers are removed. Dataset Description The provided dataset contains pairs of X and Y values, representing a relationship between two variables. Initially, the dataset includes an outlier that distorts the pattern of the data. The first scatter plot displays this outlier along with the regression line, equation, and coefficient of determination (R²). Scatterplot with Outlier X Y 1.01 2.8482 1.07 2.5252 1.16 2.842 1.19 2.4752 1.19 3.5343 … … Outlier Detection and Removal To identify and remove the outlier, residual analysis was conducted by calculating the difference between observed and predicted Y values. Residuals falling outside 1.5 times the Interquartile Range (IQR) from the first and third quartiles were considered outliers. After outlier detection, one data point was identified and removed from the dataset. Scatterplot without Outlier X Y 1.01 2.8482 1.07 2.5252 1.16 2.842 1.19 2.4752 1.19 3.5343 … … Regression Analysis Comparison Comparing the regression results of the two plots reveals substantial differences in the regression line when the outlier is present versus when it is removed. Impact of Outlier on Regression Line – With Outlier: The presence of an outlier can skew the regression line towards it, leading to a less accurate representation of the relationship between variables. – Without Outlier: Removing the outlier allows the regression line to better fit the remaining data points, providing a more reliable model of the data distribution. R² Increase after Outlier Removal The coefficient of determination (R²) indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s). When an outlier is removed, R² tends to increase because the model becomes more accurate in explaining the variance in the data without being heavily influenced by extreme values. In conclusion, outliers have a significant impact on regression analysis by distorting the regression line and reducing model accuracy. Detecting and removing outliers can lead to a more precise and reliable regression model with higher explanatory power, as evidenced by the increase in R² after outlier removal. Researchers and analysts should be vigilant in identifying and addressing outliers to ensure the validity and robustness of their regression analyses. This question has been answered. Get Answer
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