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The student was concerned that observation #45, which has an extremely large residual (~ -60), may be biasing their estimate of the slope of this relationship. Do you have this same concern? Why or why not?

The student was concerned that observation #45, which has an extremely large residual (~ -60), may be biasing their estimate of the slope of this relationship. Do you have this same concern? Why or why not?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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The student was concerned that observation #45, which has an extremely large residual (~ -60), may be biasing their estimate of the slope of this relationship. Do you have this same concern? Why or why not? 

 

A honours student was analyzing their data concerning the total mass of song sparrows in a given nest (in grams) as a function of the distance of the nest to the nearest a food source (in meters). They generated the following diagnostic plots and regression results: mass_total 180- 150- 120- 90- ## ## Call: ## lm (formula = mass_total Residuals VIStandardized residuals ## ## Residuals: ## Min 1Q Median 3Q Max ## -61.152 -5.489 -1.008 5.942 39.578 ## ## Coefficients: ## ## (Intercept) ## distance ## --- ## Signif. codes: 0 '***' 0.001 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1 ## 40 20 0 -20 -40 -60 2.0 1.5 1.0 0.5 0.0 ## Residual standard error: 13.4 on 198 degrees of freedom ## Multiple R-squared: 0.4479, Adjusted R-squared: 0.4451 ## F-statistic: 160.6 on 1 and 198 DF, p-value: < 2.2e-16 100 TTTT Residuals vs Fitted Estimate Std. Error t value Pr(>|t|) 139.46890 -0.30582 Fitted values 100 110 Scale-Location 50 450 110 120 130 140 120 Fitted values. distance distance, data = dat) 45€ 1.85269 75.28 <2e-16 *** 0.02413 -12.68 <2e-16 *** 130 140 Standardized residuals Standardized residuals 100 NON -2 -4 NONT 45 Q-Q Residuals T T -3 -2 -1 0 1 2 3 Theoretical Quantiles Residuals vs Leverage Cook's distaste 0.000 0.005 69 119 0.010 0.015 Leverage ..
Transcribed Image Text:A honours student was analyzing their data concerning the total mass of song sparrows in a given nest (in grams) as a function of the distance of the nest to the nearest a food source (in meters). They generated the following diagnostic plots and regression results: mass_total 180- 150- 120- 90- ## ## Call: ## lm (formula = mass_total Residuals VIStandardized residuals ## ## Residuals: ## Min 1Q Median 3Q Max ## -61.152 -5.489 -1.008 5.942 39.578 ## ## Coefficients: ## ## (Intercept) ## distance ## --- ## Signif. codes: 0 '***' 0.001 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1 ## 40 20 0 -20 -40 -60 2.0 1.5 1.0 0.5 0.0 ## Residual standard error: 13.4 on 198 degrees of freedom ## Multiple R-squared: 0.4479, Adjusted R-squared: 0.4451 ## F-statistic: 160.6 on 1 and 198 DF, p-value: < 2.2e-16 100 TTTT Residuals vs Fitted Estimate Std. Error t value Pr(>|t|) 139.46890 -0.30582 Fitted values 100 110 Scale-Location 50 450 110 120 130 140 120 Fitted values. distance distance, data = dat) 45€ 1.85269 75.28 <2e-16 *** 0.02413 -12.68 <2e-16 *** 130 140 Standardized residuals Standardized residuals 100 NON -2 -4 NONT 45 Q-Q Residuals T T -3 -2 -1 0 1 2 3 Theoretical Quantiles Residuals vs Leverage Cook's distaste 0.000 0.005 69 119 0.010 0.015 Leverage ..
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