Linear equations for price and processor speed
Not what you're looking for?
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.
Purchase this Solution
Solution Summary
The solution examines linear equations for price and processor speeds.The correlation is determined.
Solution Preview
Dear Student,
The solutions are outlined below.
1. 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.
Let the relationship between speed and price be modeled by:
Price = A x Speed + B where A and B are some constants.
We can find A and B by using simple linear regression by the method of least squares.
Let sum of all speeds be spsum = 2 + 1.6 + 1.6 + 1.8 + 2.0 + 1.2 + 2.0 + 1.6 + 2.0 + 1.6 + 1.0 + 1.4 = 19.8
Let sum of all prices be prsum = 2689 + 1229 + 1419 + 2589 + 2849 + 1349 + 2929 + 1849 + 2819 + 2669 + 1249 + 1159 = 24798
Let the sum of the squares of all speeds be sqsum = 2^2 + 1.6^2 + ............1.4^2 = 33.88 where ^ means to the power of.
Let the sum of the squares of all prices be psqsum = 2689^2 + 1229^2 + .....1159^2 = 57365692
Sum of the products of price and speed is spprsum = 2x2689 + 1.6x1229 + 1.8x1419 + ...
Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.