(Solved): Male crickets chirp by rubbing their front wings together, and their chirping is temperature depen ...

Male crickets chirp by rubbing their front wings together, and their chirping is temperature dependent. The table below shows the number of chirps per second for a cricket, recorded at 10 different temperatures. (a) Find the least-squares regression line relating the number of chirps to temperature. (Round all numerical values to four decimal places.) $$\tilde{y}=$$ (b) Do the data provide sufficient evidence to indicate that there is a linear relationship between number of chirps and temperature? (Test at the $$?=0.05$$ level of significance.) State the null and alternative hypotheses. $$\begin{array}{l}{H}_0:?=0\text{ versus }{H}_a:?<0\\ H_0:?=0\text{ versus }{H}_a:??=0\\ H_0:??=0\text{ versus }{H}_a:?=0\\ H_0:?=0\text{ versus }{H}_a:?>0\\ H_0:??0\text{ versus }{H}_{\mathrm{a}}:?>0\end{array}$$ Find the test statistic. (Round your answer to three decimal places.) $$\mathrm{t}=$$ Find the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) $$\text{ t }>$$ $$t?$$ State your conclusion. $$H_0$$ is rejected. There is sufficient evidence to indicate that $$y$$ and $$x$$ are linearly related. $$H_0$$ is not rejected. There is sufficient evidence to indicate that $$y$$ and $$x$$ are linearly related. $$H_0$$ is rejected. There is insufficient evidence to indicate that $$y$$ and $$x$$ are linearly related. $$H_0$$ is not rejected. There is insufficient evidence to indicate that $$y$$ and $$x$$ are linearly related. (c) Calculate $$r^2$$. (Round your answer to three decimal places.) $$r^2=$$ What does this value tell you about the effectiveness of the linear regression analysis? $$r^2$$ is the proportion of the total variation in $$y$$ that is accounted for using the independent variable $$x$$ in a linear regression. A high value of $$r^2$$ indicates a more effective model. $$r^2$$ is the proportion of the total variation in $$y$$ that is unacoounted for using the independent variable $$x$$ in a linear regression. A high value of $$r^2$$ indicates a more effective model. $$r^2$$ is the proportion of the total variation in $$x$$ that is unaccounted for using the independent variable $$y$$ in a linear regression. A low value of $$r^2$$ indicates a more effective model. $$r^2$$ is the proportion of the total variation in $$x$$ that is accounted for using the independent variable $$y$$ in a linear regression. A low value of $$r^2$$ indicates a more effective model. You may need to use the appropriate appendix table or technology to answer this question.