Question

rainfall and corn crop yield reported for the 38 years from 1890 through 1927 give us the scatterplot shown below with an r = 0.0426. yield is the number of ears of corn measured in metric tons per hectare, rainfall is in inches. based on corn crop yield from ezekiel, m. and k. a. fox. (1959). methods of correlation and regression analysis. wiley: new york. the following edited output is available: the regression equation is yield = 23.55 + 0.78 rain predictor coef se coef t p constant 23.55 3.24 rain 0.7755 0.2938 2.6391 0.0122 which of the following is an appropriate conclusion based on the output? a. the data provide extremely strong evidence that crop yield is linearly related to rainfall. b. the data do not provide sufficient evidence to conclude that crop yield is linearly related to rainfall. c. the data provide moderately strong evidence that crop yield is linearly related to rainfall.

Explanation:

Step1: Analyze the correlation coefficient

The correlation coefficient $r = 0.0426$. A value of $r$ close to 0 indicates a weak linear relationship.

Step2: Analyze the p - value

The p - value for the Rain variable is 0.0122. In general, if the p - value is small (commonly less than 0.05), we reject the null hypothesis of no linear relationship. But considering the very low $r$ value, the linear relationship is still weak.

Answer:

B. The data do not provide sufficient evidence to conclude that crop yield is linearly related to rainfall.