Predicting Cost of Electricity Given below are measurements from Triola’ s home.
ID: 3266654 • 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 cost of electricity and the kWh of electricity consumed.
r =
b. What percentage of the variation in cost can be explained by the linear relationship between electricity consumption (in kWh) and cost?____%.
c. Find the equation of the regression line that expresses cost (y) in terms of the amount of electricity consumed (in kWh).
y ˆ =b 0 +b 1 x =
y -Intercept, b0 =
Slope, b 1 =
d. What is the best predicted cost for a time when 3000 kWh of electricity is used?
The best predicted cost for a time when 3000 kWh of electricity is used would be ________
Explanation / Answer
a.
test statistics={r(sqrt(n-2)}/(sqrt(1-r2))
t = 6.4149, df = 8, p-value = 0.0002059
so, r is not zero
2. r^2=0.8372342
so, 83.72 percent is explained.
3.y=-51.6943 +0.1129*x
b0=-51.6943 , when x=0 at that point cost
b1=0.1129 is the rate at which cost increases with increase of one unit in x.
d.cost=-51.6943 +0.1129*300=-17.824