91影视

_{$,{尾}_0$}is negative, indicating that the y-intercept is negative for the regression equation, while ${尾}_1,{尾}_2,and{尾}_3$are all positive, indicating that the variables are all positively related to the dependent variable.

Here, ${尾}_1$is positive, which implies that for every 1-unit increase in the predictor variable, the outcome variable will increase by the _{${尾}_1$}value (here,25), similarly _,${尾}_{2}and{尾}_3$ are also positive; thus, for every 1 unit increase in the predictor variable, the outcome variable will increase by the ${尾}_2$value (here,100) and ${尾}_3$value (here,10).

$H_0\text{:}{尾}_1={尾}_2={尾}_3=0$

Ha : At least one of the parameters ${尾}_1,{尾}_2,{尾}_3$is non-zero.

Here, the F test statistic$=\frac{\frac{R^2}{k}}{\frac{\left(1-R^2\right)}{\left[n-\left(k+1\right)\right]}}=\frac{\frac{0.65}{3}}{\frac{1-0.65}{30-\left(3+1\right)}}=16.661$

Value of $F_{0.05,28,28}$is 1.901

H₀

is rejected if F statistic > $F_{0.05,28,28}$. For$伪=0.05$ , since$F>F_{0.05,28,28}$ sufficient to reject H₀ at 95% confidence interval.

Therefore,${\mathbf{尾}}_{\mathbf{1}}鈮�{\mathbf{尾}}_{\mathbf{2}}鈮�{\mathbf{尾}}_{\mathbf{3}}鈮�\mathbf{0}$which means we accept the alternative hypothesis.

$$\begin{gathered} H_0\text{:}{尾}_1=0 \\ {H}_a\text{:}{尾}_1鈮�0 \end{gathered}$$

Here, the t-test statistic

Value of $t_{0.05,24,24}$is 1.699

H₀ is rejected if t statistic >$t_{0.05,24,24}$. For , since $t>t_{0.05,24,24}$sufficient evidence to reject at a 95% confidence interval.

Therefore,localid="1660801540094" ${\mathit{尾}}_{\mathbf{1}}\mathbf{=}\mathbf{0}$

The regression equation is $\hat{y}=-105+25x_1+100x_2+10x_3$.

The prediction value of daily attendance on sunny weekdays at95⁰F can be calculated when $x_1=0,x_2=1and{x}_3=95$

$$\begin{gathered} \hat{y}=-105+25\left(0\right)+100\left(1\right)+10\left(95\right) \\ =900 \end{gathered}$$

Therefore, the predicted attendance on a sunny weekday at a temperature of 95⁰Fis 900.

The 90% prediction interval for daily attendance is (645, 1245), indicating that the future values of the dependent variables will fall between the interval. From part d, the value of 900 is also falling into the prediction interval.