Final answer:
To construct a 95% confidence interval estimate of the expected heating cost for buildings with 200,000 square feet of floor space, we can use the equation of the least squares line. The upper bound for the 95% confidence interval estimate is 659.08.
Step-by-step explanation:
To construct a 95% confidence interval estimate of E(y200), the expected heating cost for buildings with 200,000 square feet of floor space, we can use the equation of the least squares line. The equation is y = mx + b, where y represents the heating cost and x represents the floor area. The slope (m) is 2.2 and the intercept (b) is 182. Plugging in x = 200, we can calculate the estimated heating cost:
E(y200) = 2.2(200) + 182 = 604
Now, to find the upper bound of the confidence interval, we need to find the margin of error. The formula for the margin of error is given by:
Margin of Error = t * (Standard Error)
Since we need a 95% confidence interval, we can find the t-value for a two-tailed test at a significance level of 0.05 and four degrees of freedom (n-2=3). Using a t-table or calculator, we find t = 3.182. The standard error can be calculated as:
Standard Error = sqrt((sum of squared residuals) / (n-2)) = sqrt(300) = 17.32
Finally, plugging in the values, we get:
Margin of Error = 3.182 * 17.32 = 55.08
Therefore, the upper bound for the 95% confidence interval estimate of E(y200) is:
E(y200) + Margin of Error = 604 + 55.08 = 659.08