Create a residual plot and comment on the appropriateness of the model. $(5$ marks$)$

$$Even though the source of the data is reliable, describe at least two biases or mistakes that could have been mi collecting the data that would affect any conclusions. Include questions you may ask to investigate these potenti issues. $(6$ marks$)$

The next $2$ questions refer to the following data set. Show any relevant calculations or spreadsheet formulas that you u while responding to the questions.

X

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

y

$7\mathrm{.}2$

$6\mathrm{.}2$

$2\mathrm{.}4$

$17\mathrm{.}0$

$35\mathrm{.}1$

$60\mathrm{.}0$

$96\mathrm{.}6$

$133\mathrm{.}5$

$180.$

$$Create a scatter plot of the data, and create a residual plot for a line of best fit. Based on your observation, does the data follow a linear pattern? $(5$ marks$)$

$$While we used a line of best fit to calculate residuals earlier, you can actually use any model to calculate residuals

and create a residual plot. Use the estimate est $=3\mathrm{.}3..?$

$-9\mathrm{.}4$a $-0\mathrm{.}1$ to calculate a new set of residuals, using

a formula or a calculator. Explain your steps, then create a residual plot using this new model and assess its validity.

$(6$ marks$)$

For each of the following relationships, predict whether they are cause$-$effect, accidental, or common$-$cause. Explain your conclusion and, if they are cause$-$effect, explain which causes the other and why.

$13.$ Students with a shorter travel time to school have lower test scores. $(3$ marks$)$

wanna lilalu to carn a PhD when they grow up$.(3$ marks$)$