In a study to determine the relationship between ambient outdoor temperature and

Question

In a study to determine the relationship between ambient outdoor temperature and the rate of evaporation of water from soil, measurements of average daytime temperature in °C and evaporation in mm/day were taken for 15 days. The results are shown in the following table

A. Compute 95% confidence intervals for ?0 and ?1. Round the answers to three decimal places

B. Predict the evaporation rate when the temperature is 20 °C. Round the answer to two decimal places

C. Find a 95% confidence interval for the mean evaporation rate for all days with a temperature of 20 °C. Round the answers to three decimal places

D. Find a 95% prediction interval for the evaporation rate on a given day with a temperature of 20 °C. Round the answers to three decimal places

I'm having trouble finding Xi and X(Bar) and Yi and Y(Bar). I know the averages but I dont know how to find the other values

Temp. Evap. 11.5 2.3 21.5 4.4 16.5 5 23.6 4.1 19.1 6 21.6 5.9 31 4.8 18.9 3 24.2 7.1 19.1 1.6 11.8 3.8 24.2 5 15.8 2.6 26.8 8 24.8 5.4

Explanation / Answer

Consider Temperature to be the variable X, and Evaporation to be Y.

Then every value of X is Xi, where i = 1 to n; here n= 15 ; i.e., the first value of X is X1 , second X2 and so on.

Similarly for the variable Y.

Now X-bar and Y-bar denote the means of X and Y respectively.

You already know the averages. Well those are the means, i.e. X-bar and Y-bar.

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