Is there a correlation between the Outside Temperature and Natural Gas Consumpti

Question

Is there a correlation between the Outside Temperature and Natural Gas Consumption for a typical house The dataset contained monthly observations beginning in September 1990, and continuing through May 1997. The variables were the mean temperature per month in Boston and the corresponding natural gas consumption. Below is the software output. From the software output, determine the r. r = ___ From the Statistics, how well do the points adhere to a straight line? Identify the statistic used and Explain From the Statistics, how good is the equation in predicting the Gas usage from the temperature? Identify the statistic used and Explain The following table is a data set that is generated for an object that is "thrown" upward into the air. of the distances are approximate.

Explanation / Answer

Let's denote gas usage by Y and temp by X.

(6)

r = sqrt(R2) = sqrt(0.864) = +/- 0.929

So, r = -0.929, here we choose the -ve value because the plot shows a downward trend.

(7)

Since the r value ( Pearson coefficient ) is very close to 1, this means that there is a strong linear relationship between X and Y.

(8)

The equation is a really good fit. This is evident from the data for R2, which is 86.4%, which means that 86.4% of the total variability in Y is explained by the predicted linear relationship between X and Y.

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