# Linear regression questions

Please use Excel when necessary:

Management has collected data on the size of five work groups(X) and the number of complaints per month (Y) received by the organization from each group. A regression was run using as the independent variable the size of the work group(number of employees in the work group) to predict the number of registered complaints. Suppose the regression equation from the data is: Y = 2 + 2.25(X). Given a new work group that consisted of 8 employees, How many complaints could management expect?

a) 3

b) 10

c) 20

d) 16

If the level of confidence is decreased from 95% to 90%, the width of the corresponding confidence interval will:

a) be increased

b) be decreased

c) Stay the same

d) The level of confidence does not have an effect on the width of the interval

https://brainmass.com/statistics/linear-regression/linear-regression-questions-modelled-21031

## SOLUTION This solution is **FREE** courtesy of BrainMass!

The calculations in this problem are very simple and it's not necessary to use an Excel sheet to do them. Please see the attached Word document for the solutions to these questions and detailed explanations.

1) Management has collected data on the size of five work groups(X) and the number of complaints per mont (Y) received by the organization from each group. A regresion was run using as the independent variable the size of the work group(number of employees in the work group)to predict the number of registered complaints. Suppose the regression equation from the data is: Y = 2 + 2.25(X). Given a new work group that consisted of 8 employees, How many complaints could management expect? a) 3, b) 10, c) 20, d) 16,

Solution

It is not necessary to use Excel to do this problem. The key here is in knowing the interpretation of the prediction equation, . The value of Y for any given value of X is an estimation of the expected value of complaints per month (Y) for the given value of work group size (X). All you have to do to find the estimate of the expected number of complaints for a work group of size 8 is substitute the value 8 for X in the prediction equation.

The best estimate of the number of complaints management could expect given a new work group of 8 employees is 20. The answer to the question is (c).

2) Problem # 2 If the level of confidence is decreased from 95% to 90%, the width of the corresponding confidence interval will: a) be increased, b) be decreased, c) Stay the same, d) The level of confidence does not have an effect on the width of the interval

Solution:

Any confidence interval, whether in a regression situation as this or in any other situation has the following characteristic: Increasing confidence increases the width of the interval and decreasing confidence decreases the width of the interval.

To see why this is true in the context of this problem, consider the following equation for the confidence interval in a simple linear regression context.

For 95% confidence interval, is the 97.5th percentile of a t distribution. For a 90% interval, is the 95th percentile of the t distribution. Since the 95th percentile is less than the 97.5th percentile, the number to the right of the sign in the equation decreases when going from 95% to 90% confidence. The width of the interval therefore decreases and the correct answer is (b).

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