The table displays data taken from two quantitative variables x and y. The residual plot from the least-squares regression model appears below the table.
a. Is the least-squares regression model appropriate? Explain.
b. An exponential and quadratic model were each fitted to the data. The residual plots for each appear below.
Which model is more appropriate? Explain.
c. Calculate the appropriate model for the relationship between x and y.
d. Would it be appropriate to predict y when x=4 or when x=14 ? Explain.
e. Using the model you selected, calculate and interpret the residual for the observation x=1.10, y=30.17.
A scatterplot and residual plot display the relationship between two quantitative variables x and y.
a. The standard deviation of the residuals is s=58.8. Interpret this value.
b. Suppose the standard deviation of the residuals was halved. Sketch a possible residual plot with the standard deviation of the residuals halved.
c. r²=0.60. Interpret this value. What does this mean for the fit of the least-squares regression model?
d. The correlation is 0.80. What does this tell you about the relationship between x and y