12.66 Can the consumption of water in a city be predicted by air temperature? Th
ID: 3224147 • Letter: 1
Question
12.66 Can the consumption of water in a city be predicted by air temperature? The following data represent a sample of a day's water consumption and the high temperature for that day. Temperature Water Use (millions of gallons) degrees Fahrenheit) 103 219 39 56 107 129 50 96 184 90 150 112 Develop a least squares regression line to predict the amount of water used in a day in a city by the high temperature for that day. What would be the predicted water usage for a temperature of 100%? Evaluate the regression model by calculating se, by calculating r and by testing the slope. Let a 01Explanation / Answer
Solution:
The required regression analysis for the given data for dependent variable water use and independent variable temperature is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.954052627
R Square
0.910216416
Adjusted R Square
0.895252485
Standard Error
17.88775727
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
19463.04384
19463.04384
60.82736097
0.000234226
Residual
6
1919.831161
319.9718602
Total
7
21382.875
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-54.35604265
24.23708914
-2.242680313
0.066103001
-113.6620632
4.949977875
Temperature
2.401066351
0.307860999
7.799189763
0.000234226
1.647757626
3.154375076
The correlation coefficient between the dependent variable water use and independent variable temperature is given as 0.9541, which means there is strong positive linear relationship or association exists between the dependent variable water use and independent variable temperature. The value of the coefficient of determination or the R square is given as 0.9102, which means about 91.02% of the total variation in the dependent variable water use is explained by the independent variable temperature. The standard error Se is given as 17.8878. The p-value for overall regression model is given as 0.000234 which is less than alpha value 0.01, so we reject the null hypothesis that the given regression model is not statistically significant. This means we conclude that the given regression model is statistically significant.
The regression equation is given as below:
Water use = -54.3560 + 2.4011*Temperature
The predicted water use for temperature = 100 is given as below:
Water use = -54.3560 + 2.4011*100
Water use = 185.754
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.954052627
R Square
0.910216416
Adjusted R Square
0.895252485
Standard Error
17.88775727
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
19463.04384
19463.04384
60.82736097
0.000234226
Residual
6
1919.831161
319.9718602
Total
7
21382.875
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-54.35604265
24.23708914
-2.242680313
0.066103001
-113.6620632
4.949977875
Temperature
2.401066351
0.307860999
7.799189763
0.000234226
1.647757626
3.154375076
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.