Is there any concerns with respect to the assumptions underlying a linear regression using these data? Explain what the concerns are and what can be done to address them.

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Is there any concerns with respect to the assumptions underlying a linear regression using these data? Explain what the concerns are and what can be done to address them.

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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