Also, the SE (standard error) of the estimated slope is 0.03871. (d) You now have the estimated slope and its SE (standard error). To compute the 95% c.i. of the true slope, what's the appropriate t-value that we need to use?
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The degrees of freedom for a simple linear regression is calculated as the number of observations (n) minus 2 (df = n - 2). You need to know the sample size (n) to calculate this. Show more…
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(a) Give the standard error of the slope, $\mathrm{SE}_{b}$. Interpret this value in context. (b) Find the critical value for a $99 \%$ confidence interval for the slope of the true regression line. Then calculate the confidence interval. Show your work. (c) Interpret the interval from part (b) in context. (d) Explain the meaning of "99\% confident" in context.
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Inference for Linear Regression
Critical Thinking: Using Information from a Computer Display to Find a Confidence Interval Refer to the Minitab printout regarding prehistoric pottery. (a) The standard error $S_{e}$ of the linear regression model is given in the printout as "S." What is the value of $S_{e}$ ? (b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for $b$ is $S_{e} / \sqrt{\Sigma x^{2}-\frac{1}{n}(\Sigma x)^{2}}$ From the Minitab display, what is the value of the standard error for the slope $b ?$ (c) The formula for the margin of error $E$ for a $c \%$ confidence interval for the slope $\beta$ can be written as $E=t_{c}(\mathrm{SE}$ Coef $)$. The Minitab display is based on $n=9$ data pairs. Find the critical value $t_{c}$ for a $95 \%$ confidence interval in Table 6 of Appendix II. Then find a $95 \%$ confidence interval for the population slope $\beta$.
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