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# Correlation Coefficient Of Linear Functions

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Let X1, X2, and X3 be random variables with equal variances but with correlation coefficients rho12=0.3, rho13=0.5, and rho23=0.2 Find the correlation coefficient of the linear functions Y=X1+X2 and Z=X2+X3.

https://brainmass.com/statistics/correlation/correlation-coefficient-linear-functions-44863

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Let X1, X2, and X3 be random variables with equal variances but with correlation coefficients ...

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The solution is comprised of a detailed step by step explanation of how to find the correlation coefficient of linear functions.

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## Linear equations for price and processor speed

The following data show the retail price for 12 randomly selected laptop computers along with their corresponding processor speeds in gigahertz.

Computer Speed Price
1 2.0 \$ 2,689
2 1.6 1,229
3 1.6 1,419
4 1.8 2,589
5 2.0 2,849
6 1.2 1,349
7 2.0 2,929
8 1.6 1,849
9 2.0 2,819
10 1.6 2,669
11 1.0 1,249
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-underpriced.
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

2. What is correlation? Does correlation prove causation? Why or why not? Explain and provide examples to support your explanation.

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