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Regression Analysis and Hypothesis Test

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53. The following data show the retail price for 12 randomly selected laptop computers along with their corresponding processor speeds in gigahertz.
Computer Speed Price Computer Speed Price
1 2.0 2,689 7 2.0 2,929
2 1.6 1,229 8 1.6 1,849
3 1.6 1,419 9 2.0 2,819
4 1.8 2,589 10 1.6 2,669
5 2.0 2,849 11 1.0 1,249
6 1.2 1,349 12 1.4 1,159

a. Develop a linear equation that can be used to describe how the price depends on the processor speed.

b. Based on your regression equation, is there one machine that seems particularly over or under-priced?

c. Compute the correlation coefficient between the two variables. At the .05 significance level conduct a test of hypothesis to determine if the population correlation could be greater than zero.

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Solution Summary

The solution provides step-by-step method of performing a Regression Analysis and Correlation Hypothesis Test. Regression Analysis (Correlation Coefficient, Coefficient of Determination, Covariance, Regression Equation etc.) have been performed in EXCEL. All the steps involved in Correlation Hypothesis Test (formulation of Null and Alternate Hypothesis, Selection of Significance Level, Choosing the appropriate Test-Statistic, Decision Rule, Calculation of Test-Statistic, P-Value and Conclusion) have been explained in details.

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Regression Analysis: Hypothesis Testing Example Problem

A research would like to examine the effects of humidity on eating behavior. It is known that laboratory rats normally eat an average of µ = 21 grams of food each day. The research selects a random sample of n = 16 rats and places them in a controlled atmosphere room in which the relative humidity is maintained at 90%. The daily food consumption scores for rats are as follows:

14, 18, 21, 15, 18, 18, 21, 18
16, 20, 17, 19, 20, 17, 17, 19

a) Can the researcher conclude that humidity has a significant effect on eating behavior? Use a two-tail test with a = .05.

b) Compute the estimated d and r 2 to measure the size of the treatment effect.

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