Figure 27 (page 267) gives the MINITAB output of residual diagnostics that are o

Question

Figure 27 (page 267) gives the MINITAB output of residual diagnostics that are obtained when the simple linear regression model is fit to the Fresh detergent demand data in Exercise 3.9 Interpret the diagnostics and determine if they indicate any violations of the regression assumptions Figure 27 (for Exercise 5.5) MINITAB residual diagnostics for the Fresh detergent demand data Residualo Versus the Pitted Values Histagras of the Reslduals 025 0 50 02 02 85 Normal Probability Plot of the Residuals freeponse is Demand) 30 05319 AD 90 70 60 30 10 0,5 0.0 0.5 1.0

Explanation / Answer

Regression assumtion :

a ) Normality -Regression assumes that the residuals are normally distributed.

b) Homoscedasticity–This assumption states that the variance of error terms are similar across the values of the independent variables. Residuals are equal variance

c )The regression model is linear in parameters.

d ) The mean of residuals is zero.

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1) Histogram is not symmetric , wo we can't say that data follow normal distribution .

2) a) The points on the residual plot above not appear to be randomly scattered around zero,

so assuming that the error terms have a mean of zero is not reasonable.

b ) The vertical width of the scatter does appear to increase or decrease across the fitted values, so we can assume that the variance in the error terms is not constant.

3) For normal probability plot :

Null hypothesis

H: Data follow a normal distribution

Alternative hypothesis :

H: Data do not follow a normal distribution

So here p- value = 0.160 > alpha =0.05

the p-value is 0.160, which is greater than the significance level of 0.05,

the decision is to fail to reject the null hypothesis.

You cannot conclude that the data do not follow a normal distribution.

So here , volatation of regression assumptions are not satisfied . This graph tells us we should not use the regression model that produced these results.

Null hypothesis

H: Data follow a normal distribution

Alternative hypothesis :

H: Data do not follow a normal distribution

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