Question

In: Statistics and Probability

Use the output below to answer the following questions regarding the association between carbon dioxide levels...

Use the output below to answer the following questions regarding the association between carbon dioxide levels and amount of coal used.

Estimate Std. Error. t value. P r(> |t|

Intercept 6.166678. 2.171695. 2.84 0.00571

Coal 0.030171. 0.002976 10.14. 4.52e-16

-Create a 98% estimate for the independent variable.

- Is the explanatory variable significant at α = 0.01? -

Suppose the correlation is 0.7478824. Determine the value of the coefficient of determination and explain what this value represents.

- What is the response variable when the explanatory variable is 700? (NOTE: This value is within the range of the explanatory variable)

Expert Solution

-Create a 98% estimate for the independent variable

Critical t- score for 98% confidence is t = 2.4033

Lower limit of the confidence interval = b - t * SE = 0.030171 - 2.4033 * 0.002976 = 0.0230

Upper limit of the confidence interval = b + t * SE = 0.030171 + 2.4033 * 0.002976 = 0.0373

The 98% confidence interval for the slope is [0.0230, 0.0373]

- Is the explanatory variable significant at α = 0.01?

p- value (4.52e-16) < α (0.01), so the explanatory variable is significant

- Suppose the correlation is 0.7478824. Determine the value of the coefficient of determination and explain what this value represents

r^2 = 0.7478824^2 = 0.5593. This means about 55.93% of the variation in y is explained by the variation in x using this model

- What is the response variable when the explanatory variable is 700?

When x = 700, y = 0.030171 * 700 + 6.166678 = 27.286378

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