Predicting Cost of Electricity Given below are measurements from Triola’ s home.
ID: 3266657 • Letter: P
Question
Predicting Cost of Electricity Given below are measurements from Triola’ s home.
kWh: 3375, 2661, 2073, 2579, 2858, 2296, 2812, 2433, 2266, 3128.
Heating Degree Days: 2421, 1841, 438, 15, 152, 1028, 1967, 1627, 537, 26.
Average Daily Temp: 26, 34, 58, 72, 67, 48, 33, 39, 66, 71.
Cost (dollars): 321.94, 221.11, 205.16, 251.07, 279.8, 183.84, 244.93, 218.59, 213.09, 333.49.
a. Use a 0.05 significance level to test for a linear correlation between the average daily temperature and the cost. r =
b. What percentage of the variation in cost can be explained by the linear relationship between cost and average daily temperature? _____%.
c. Find the equation of the regression line that expresses cost (y) in terms of the average daily temperature.
y ˆ =b 0 +b 1 x=
y -Intercept, b0 =
Slope, b1=
d. What is the best predicted cost at a time when the average daily temperature is 40? The best predicted cost for a time when the average daily temperature is 40 would be________
Explanation / Answer
a. test statistics= {r*sqrt(n-2)}/(sqrt(1-r2))
here t = 0.2416, df = 8, p-value = 0.8152
so, r is zero by test.
the actual computed r is 0.08510897
b. it's given by rsquared= 0.7%
c.y =234.7961 + 0.2433 *x
when x is zero y is b0
when x increases by 1 y increases by 0.2433 i.e. b1
d. 234.7961 + 0.2433 *40 =244.528 is the predicted value.