WeBWorK Standalone Renderer

For each residual plot below, decide on whether the usual assumptions:
" $Y_i=\beta_0+\beta_1 x_i+\epsilon_i, i=1,\ldots,n, \epsilon_i$ independent N(0, $\sigma^2$ ) random variables" of simple linear regression are valid or not.
If some assumptions seem invalid, choose the options(s) which indicate the most obvious departures from the model assumptions. Note : For a small sample, the normality assumption cannot be "proved", but it can be "violated" if there is an extreme residual (outlier).
Part a)

y-axis has residual, x-axis has x-variable with values 1,2,...,10. (Click on graph to enlarge)

Which is/are the best answer(s) for the residual plot (a)?

A. constant variance assumption is invalid
B. the normality assumption is invalid
C. linear relation assumption is invalid
D. assumptions seem reasonable
E. None of the above

Part b)

y-axis has residual, x-axis has x-variable with values 1,2,...,10. (Click on graph to enlarge)

Which is/are the best answer(s) for the residual plot (b)?

A. assumptions seem reasonable
B. the residuals show a pattern
C. constant variance assumption is invalid
D. linear relation assumption is invalid
E. the normality assumption is invalid
F. None of the above

Part c)

y-axis has residual, x-axis has x-variable with values 1,2,...,10. (Click on graph to enlarge)

Which is/are the best answer(s) for the residual plot (c)?

A. linear relation assumption is invalid
B. constant variance assumption is invalid
C. the normality assumption is invalid
D. the residuals show a pattern
E. assumptions seem reasonable
F. None of the above

Hint:

You can earn partial credit on this problem.