Chapter 27, Problem 28E

a)

To determine

To write the equation of the regression line.

Answer to Problem 28E

  $Temp=15.3066+0.004x$

Explanation of Solution

Given:

  

The general regression equation is,

  $\widehat{y}=b_0+b_{1}x$

Here,

  $\begin{array}{l}{b}_0=15.3066\\ b_1=0.004\end{array}$

Therefore, the equation of regression line is,

  $Temp=15.3066+0.004x$

b)

To determine

To perform hypothesis test.

Answer to Problem 28E

There is sufficient evidence that the slope is non zero and there is association between the CO₂ level and global temperature.

Explanation of Solution

Given:

  

Formula:

Test statistic:

  $t=\frac{b-{\beta }_0}{S{E}_b}$

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

Test statistic:

  $t=\frac{0.004-0}{0.0009}=4.444$

The degrees of freedom = df = 35

Therefore, p-value would be,

P-value = 0 …Using excel formula, =TDIST(4.44435,2)

Decision: P-value < 0.05, reject H₀.

Conclusion: There is sufficient evidence that the slope is non zero and there is association between the CO₂ level and global temperature.

c)

To determine

To explain whether the prediction will be accurate.

Answer to Problem 28E

The prediction done using this equation would not be accurate.

Explanation of Solution

Given:

  

The R-square = 33.4% which is less. Therefore, the prediction done using this equation would not be accurate.