# Histresidu col yellow xlabresidual main histogram of

• Test Prep
• 8

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> hist(Residu, col= "yellow", + xlab="Residual", main = "Histogram of Residual")

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Conclusion : Residual is distributed throw out the histogram and in a symmetrical way so histogram is good. > boxplot(Residu, col= "green", horizontal = TRUE, main= "Residual Boxplot", xlab="Residual") Conclusion : There is no outlier. Residual plot middle tick line is a bit shifted to the right. #2b
> lm_MaxPower<-lm(max ~ age) > lm_Fu<-lm(max~factor(age)) > anova(lm_MaxPower,lm_Fu) Analysis of Variance Table Model 1: max ~ age Model 2: max ~ factor(age) Res.Df RSS Df Sum of Sq F Pr(>F) 1 13 272.43 2 2 32.50 11 239.93 1.3423 0.5028 lack-of-fit test : Ho: E{Y} = Bo + B1X vs Ha : E{Y} =/=Bo + B1X Alpha = 0.05 F*= 1.3423 P-Value = 0.5028 > alpha so do not reject null. Conclusion : At significant level of 0.05 on degree of freedom of 13 and 2, there is evidence that the linear model is appropriate for the data. #2c : Multiple R-squared: 0.9091 R-square interpretation Approximately 90% variation of maximum heart rate can be explained by the regression on age. #3 > predict(lm_MaxPower, interval = "confidence", + newdata = data.frame(age=35), level = 0.99) fit lwr upr 1 182.128 178.5338 185.7223 We are 99% confident that the maximum heart rate when age is 35years will be between 178.5338bpm and 185.7223bpm #4 General Summary Our confidence and prediction band show a negative simple linear regression line which is supported by our final model with a negative slope. Construct and interpret of 99% confidence interval for the slope of maximum heart rate support a negative slope. True Regression line slope test show we should accept our alternative hypothesis that means at any significant level there is enough evidence that the there is a linear relation between maximum heart rate and age.

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Diagnosis of our plots show they are good and it satisfies homoscedasticity. Also lack of fit test also conclude that our linear model is appropriate for the data. Furthermore, R-square help us explain that 90% of our regression can be explained. So, I will greatly say our model is appropriate based our data and it support the equation (“max” = 220 - “age”) of the relationship between maximum heart rate and age.
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