The moisture in a wet mix of cement was considered to have an effect on the denseness of the finished product.The moisture of the mix was controlled at various levels,and the denseness of the finished product was measured.The data were entered into SPSS,and the following output was generated. The residuals from this regression analysis are plotted versus the explanatory variable.The graph is provided below. Which of the following interpretations of this residual plot is correct?
A)The fit is not good because there is no linear relationship shown in this plot.
B)The fit is good because the residuals form a pattern around the x axis.
C)The fit is good because the residuals indicate a departure from the linear regression line.
D)The fit is good because no clear pattern is evident.

Question

The moisture in a wet mix of cement was considered to have an effect on the denseness of the finished product.The moisture of the mix was controlled at various levels,and the denseness of the finished product was measured.The data were entered into SPSS,and the following output was generated.      The residuals from this regression analysis are plotted versus the explanatory variable.The graph is provided below.  Which of the following interpretations of this residual plot is correct?
A)The fit is not good because there is no linear relationship shown in this plot. 
B)The fit is good because the residuals form a pattern around the x axis. 
C)The fit is good because the residuals indicate a departure from the linear regression line. 
D)The fit is good because no clear pattern is evident.

Quizplus · Accepted Answer

The residual plot shows no clear pattern, indicating that the linear regression model is a good fit for the data. Option B is incorrect because a pattern around the x-axis would indicate heteroscedasticity, which violates the assumption of homoscedasticity in linear regression. Option C is incorrect as the residuals do not show a consistent departure from the regression line. Option A is incorrect because a lack of a linear relationship would be seen in the scatter plot of the variables, not in the residual plot.

The Moisture in a Wet Mix of Cement Was Considered