Am I missing something?
I believe the confidence interval is:
$$b_1 \pm t_c * s_{b_1} $$
I don't see the standard error of the slope coefficient though.
4
-
1$\begingroup$ None of these answers look right because the estimate of the slope is 0,350 from the table. You are right that the standard error of the estimate is not given in the table. $\endgroup$– Michael R. ChernickCommented Apr 12, 2018 at 2:02
-
$\begingroup$ Is it possible to back into the standard error based on the information given in the chart? I've done hundreds of these examples and this is the first time I've seen the possibility that the correct answer isn't there. $\endgroup$– CcSCommented Apr 12, 2018 at 2:07
-
1$\begingroup$ There is enough information provided to solve this question. The correct answer is provided. I am hesitant to provide more information because this appears to be an assessment item. Update, Never mind, I see Yoon provided the solution needed as I was working the problem. $\endgroup$– BryanCommented Apr 12, 2018 at 2:38
-
1$\begingroup$ You can eliminate two of the options immediately because the t-interval is symmetric about the coefficient estimate -- by inspection, two of the options are not centered at $\hat{\beta}_1$. Cross those out, and there's only one possible answer left. That doesn't prove that it's correct, of course, but the one that you can't immediately eliminate is indeed the correct answer in this case. In many cases a quick answer is readily obtained without much calculation. This (selecting the only not-impossible answer) is particularly important when time is pressing (under exam conditions, for example) $\endgroup$– Glen_bCommented Apr 12, 2018 at 6:41
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
You can relate the standard error of estimate (se) of the coefficient ($b_1$) and its t-statistic:
$$\eqalign{ \text{t-statistic} &= \frac{\hat b_1}{\operatorname{se}\left(\hat b_1\right)} \\ \implies \operatorname{se}\left(\hat b_1\right) &= \frac{\hat b_1}{\text{t-statistic}}, }$$
whence
$$\frac{0.35}{0.534}=0.655\ldots.$$
-
$\begingroup$ Welcome to our site! I have replaced your image with TeX markup to illustrate how you can use it in future posts here. $\endgroup$– whuber ♦Commented Apr 12, 2018 at 14:13