Question 34: Given are five observations for two variables, x and y . Please inc

ID: 3183520 • Letter: Q

Question

Question 34: Given are five observations for two variables, x and y. Please include work.

Round your answers to two decimal places.

a. Using the following equation:

Estimate the standard deviation of * when x = 3.

b. Using the following expression:

Develop a 95% confidence interval for the expected value of y when x = 3.

_____ to _____

c. Using the following equation:

Estimate the standard deviation of an individual value of y when x = 3.

d. Using the following expression:

Develop a 95% prediction interval for y when x = 3.

____ to ____

xi 1 2 3 4 5 yi 3 7 5 11 13 (xi-X)2 I n

a. Xbar = 3 and * = 7.8

Putting its value in the given equation for calculating standard deviation of y^*

sy^* = s sqrt [ 1/n + (x*- Xbar)2/(xi - xbar)2]

Here s = standard deviation of y = 4.15

so sy^* = 4.15 sqrt[ 1/5 + 0] as x* = 3 and xbar = 3

sy^* = 1.856

(ii) 95% confidence interval for the expected value of y when x = 3. so t- value for alpha = 0.05 for defree of freedom 5-1 =4 is equal to 2.776

so 95% confidence interval would be y^* +- 2.776 * sy^* = 7.8 +- 2.776 * 1.856 = (2.65,12.95)

iii) sspred = s sqrt[ 1+ 1/n + (x*- Xbar)2/(xi - xbar)2] = 4.15 * sqrt [ 1 + 1/5 + 0] = 4.546

(iv) 95% confidence interval for the expected value of y when x = 3. so t- value for alpha = 0.05 for defree of freedom 5-1 =4 is equal to 2.776

so 95% confidence interval would be y^* +- 2.776 * sy^* = 7.8 +- 2.776 * 4.546 = (0,20.42)

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