dataset Power Plant records variables which the company’s engineers believe are important factors in the operation of the plant

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Programming for Data Analysis and Visualization CA 2

Q1.The dataset “Power Plant” records variables which the company’s engineers believe are important factors in the operation of the plant. The company is interested in maximising net hourly electrical energy output (recorded as PE in the dataset). For each hour of energy output recorded, other variable “Temperature” (AT) in the range 1.81°C and 37.11°C is recorded.

Steps:

1. Run a linear regression model for PE over AT. Record the value for the slope 𝛽⌃1 and take it as the actual population parameter 𝛽1.

2. For 1000 iterations:

a. Take 50 random samples from the dataset. Run the regression model and using the expression for CI for 𝛽1, that we found in the lecture, find a 95% CI for 𝛽1.

b. Find what percentage of the CIs generated in step 2 would contain the 𝛽1

that you got in step 1.

Q2. If X1and X2 are independent random samples from the Uniform distribution U(0,1), by generating random samples find 𝑃 (|X1 − X2| < 1). Q3. If Xi𝑠 are independent random samples from the Beta distribution 𝛽(1, 1 + 𝜃), by generating random samples for 3 different values for 𝜃 find ∑10 ln(1 − Xi) 𝐸 [ j=6 ] 10 j=1 ln(1 − Xi) and show that the result is independent from 𝜃. b. Using the distribution in Q2, show that the result is even independent from the distribution of Xi𝑠.

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