# MATH 1281 DISCUSSION FORUM UNIT 8

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The Most Common Obstacles to Using Diagnostic Plots (DPs) DPs are effective graphical tools for evaluating the veracity and assumptions of statistical models. Although they can offer insightful information in a variety of ways, such as data exploration and linear model diagnosis using methods other than the built-in base R function (Kim, 2015). However, when employing DPs, there are a few common problems that can arise. Following are a few of these difficulties and solutions: Interpretation Difficulty: To understand appropriately, DPs always require a certain degree of statistical data (Smith, 2015). Now let's take a look at a QQ plot, also known as a quantile-quantile plot in this instance, which is a graphical tool for determining if a collection of data might reasonably have come from a theoretical distribution like a normal or exponential. To test the assumption that our residuals are normally distributed, for instance, we should utilize a normal QQ plot while conducting statistical analysis. As another illustration, the quantiles of a dataset can be compared to the quantiles of a typical statistical distribution using a Q-Q plot. Therefore, it will be quite difficult for you to interpret the story without having a greater understanding of the QQ plot (Ford, 2015). Outliers: whether there are any influential cases. A diagnostic plot may be distorted by outliers, and it may be challenging to ascertain how they affect the regression line (Kim, 2015), as well as to identify patterns or trends (Smith, 2015). Multivariate Data: Usually created for univariate or bivariate data, diagnostic graphs. Multivariate data visualization can be difficult and complex (Smith, 2015). How to address these Challenges? Education and Practice: Knowledge base with regular practices having experience can significantly help to solve the interpretation issues. There are many different types of instructional websites, such as online, YouTube, etc., that offer guides and useful examples on how to read different types of diagnostic plots. You can use Smith's 2015 publication "A comprehensive handbook of statistical concepts, techniques, and software tools" as an example. Treatment for Outliers: Using robust statistical techniques that are less susceptible to outliers or preprocessing the data to correct or remove outliers are two ways to deal with outliers. Dimensionality Reduction: To reduce the dimensionality of multidimensional data and make it easier to visualize, methods like Principal Component Analysis (PCA) or t-SNE can be utilized. Here's an illustration of a Q-Q plot: A scatterplot that pits two sets of quantiles against one another is known as a QQ plot. The points should form a straight line if both quantiles originated from the same distribution.
Because both sets of quantiles are drawn from normal distributions, this is a typical QQ plot. For instance, if the ordinary normal distribution has a mean of 0, then the 0.5 quantile, or 50th percentile, is 0. Meaning that half of the data are below 0, and this is regarded as the apex of the hump in the curve. The 95th percentile, or 0.95 quantile, is roughly 1.64. 95 percent of the values are below 1.64. The quantiles for a typical normal distribution are generated using the R code below, with increments of 0.01 from 0.01 to 0.99: Therefore: qnorm(seq(0.01,0.99,0.01)) Additionally, we can generate data at random using a conventional normal distribution and then calculate the quantiles. Here, we build a sample of size 200 and use the quantile() function to determine the quantiles from 0.01 to 0.99: So: quantile(rnorm(200),probs = seq(0.01,0.99,0.01)) (Ford, 2016). References: Ford, C. (2015, August 26). Understanding QQ Plots. University of Virginia Library Research Data Services + Sciences. Research Data Services + Sciences. Retrieved from https://data.library.virginia.edu/understanding-q-q-plots/ Kim, B. (2015, September 21). Understanding Diagnostic Plots for Linear Regression Analysis. University of Virginia Library Research Data Services + Sciences. Retrieved from https://data.library.virginia.edu/diagnostic-plots/ Smith, M. J. D. (2015). Statistical Analysis Handbook. A comprehensive handbook of statistical concepts, techniques and software tools. Retrieved from https://dl.icdst.org/pdfs/files/2aac38c9530d5311929878fa48492d9f.pdf