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# Regression Analysis

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An analyst would like to predict water consumption in a city based on daily temperature. She has gathered the following data for a random sample of n= 7 days.

Temperature ( C) 40 5 25 15 10 30 35
Water Consumption(million gallons) 225 25 150 100 75 125 175

Using the following sums and sums of squares and cross-products

Summation of x= 160 Summation of y= 875 SS(x)= 1042.857 SS(y)= 26,250 SS(xy)= 5,000

A) Compute the regression line to explain "water consumption" in terms of "temperature".
B) Test, at the alpha= 0.01 level of significance, whether temperature is a significant predictor of water consumption.
C) Compute the coefficient of determination of the regression model.
D) Find a 99% confidence interval for water consumption on a particular day when the temperature is 28ºC.

##### Solution Summary

Computes the regression line to explain "water consumption" in terms of "temperature", tests whether temperature is a significant predictor of water consumption, computes the coefficient of determination of the regression model and finds a 99% confidence interval for water consumption on a particular .

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An analyst would like to predict water consumption in a city based on daily temperature. She has gathered the following data for a random sample of n= 7 days.

Temperature ( C) 40 5 25 15 10 30 35
Water Consumption(million gallons) 225 25 150 100 75 125 175

Using the following sums and sums of squares and cross-products

Σx= 160 Σy= 875 SS(x)= 1042.857 SS(y)= 26,250 SS(xy)= 5,000

n= 7
Σx= 160
Σy= 875
SS(x)= 1042.857
SS(y)= 26250
SS(xy)= 5000

See the answer on the following pages
A) Compute the regression line to explain "water consumption" in terms of "temperature".

Regression equation: Y=a+bX
b=SS(xy)/ SS(x)= 4.7945 =5000/1042.857

ΣY=na+bΣX
or 875=7*a + 4.7945*160
or ...

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