Referring to Question 2 , the data in the business database for the year 2015 ar

Question

Referring to Question 2 , the data in the business database for the year 2015 are given in the table . The two quantities are related by the formula (to three decimal places). Gas = (-2.2921*Temp) + 234.489.

a, Suppose the explanatory (x) variable and response (y) variable were switched. How would the correlation coeficient be affected?

b, Interpret the slope in the context of the excercise

c, interpret the Y intercept in the context of the exercise. Does this seems like an accurate representation for the situation? Explain.

d, How many therms of gas use does the regression line predict for January, when the temperature was 39.0 degrees Fahrenheit?

e, What is the residual for January?( temp 39 degrees Fahrenheit)

f, Interpret this residual in context.

T A scaterptiot of the duta is given below Tomperature Gas Used Fahrenhelt (Therms) Jan-13 158 119 384 Mar-13 Aps-13 May 13 ao 1 Aug-13 Sep 13 Od 13 08 Nov 13 550 Dec 13 790 19

Explanation / Answer

Regression equation:

Gas = (-2.2921*Temp) + 234.489

a) Slope is negative. so, correlaiton coefficient trend is also negative.

b) Interpret slope: For every additional unit of Temp, Gas decreases by -2.2921 units.

c) To interpret intercept, At zero termperature the minimum gas output is 234.489 units.

d) Temp= 39

Gas = (-2.2921*Temp) + 234.489= -2.2921*39+ 234.489= 145.101

e) Residual value for temp= 39

Actual value(Yi)=116

Predicted value= 145.101

Residual value= Actual- Prediction= 116-145.101= -29.101

f) The difference between the observed value and predicted value at temperature 39 is -29.101.

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