Chapter 4 Notes Stats
Chapter 4 Notes Stats STAT 145
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This 6 page Class Notes was uploaded by Michaela Zerbo on Monday September 26, 2016. The Class Notes belongs to STAT 145 at Rochester Institute of Technology taught by Professor Nilay Sapio in Fall 2016. Since its upload, it has received 20 views. For similar materials see Intro to Stats in Statistics at Rochester Institute of Technology.
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Date Created: 09/26/16
1 STAT 145 Introduction to Statistics 1 Chapter 4 - Describing Relations between 2 Variables Terms ormulas 4.1 Scatter Plots and Correlations Objectives: Understand Scatter plots and Linear Correlations Scatter Plots: Shows relationship between two quantitative variables 2 Pearson Product Moment Correlation Coefficient ® Measure of strength and direction of the linear relation between 2 quantitative variables 3 Residuals: The difference between observed and predicted value of Y You should analyze residuals for: ● Decide if it’s appropriate to use for linear models ● See if the variance of the residuals is consistent ● Check for outliers 4 Outliers vs. Influential Observations Case 1: Large Y value Case 2: Large Y value and X value (follows the pattern in the increasing slant) Case 3: Large X value and not consistent with the slant ★ Influence is affected by 2 factors ○ Residual ■ Relative vertical position of observation ○ Leverage ■ Relative horizontal position of the observation Coefficient of Variance (CV): Calculates a unit-less standardized measure of dispersion that we can use to compare 2 different distributions Bivariate Data (Qual): It’s to summarize the relationship between 2 qualitative data Conditional Distribution: A relative frequency of each category of the response variable for a given value of the explanatory variable in the contingency table 5 Contingency Table High School Students and Favorite Sports In order to get the Frequency Marginal Distribution for the column is to add the count of Male and Female Basketball EX. 105 + 115 = 220 Football EX. 150 + 103 = 253 Soccer EX. 150 + 179 = 329 Then add up the 3 totals 220 + 253 + 329 = 802 In order to get the Frequency Marginal Distribution for the row is to add all of the specific gender Female EX. 105 + 150 + 150 = 405 Male EX. 115 + 103 + 179 = 397 Then add the 2 totals 405 + 497 = 802 To find the Relative Frequency Marginal Distribution, you need to take the total for the row and divide it by the total of the Frequency Marginal Distribution Basketball EX. 220 / 802 = .274 Football EX. 253 / 802 = .315 Soccer EX. 329 / 802 = .410 To find the Relative Frequency Marginal Distribution, you need to take the total for the row and divide it by the total of the Frequency Marginal Distribution Female EX. 405 / 802 = .505 Male EX. 397 / 802 = .495 6
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