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40 Cards in this Set
- Front
- Back
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A numerical measure of the strength of the association between two variables representing quantitative data:
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the linear correlation coefficient r
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Paired sample data is aka:
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bivariate data
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This data is used to find the value of r:
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paired sample data
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The value of r is used to conclude:
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that there is or isn't a linear correlation between two paired variables.
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A correlation exists between two variables when:
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the values of one variable are somehow associated with the values of the other variable.
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This measures the strength of the linear correlation between the paired quantitative x-and y-values in a sample.
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The linear correlation coefficient r
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The linear correlation coefficient is sometimes referred to as:
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the Pearson product moment correlation coefficient in honor of Karl Pearson who originally developed it.
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The linear correlation coefficient r is calculated using _________ data.
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sample data.
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∑ denotes:
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addition of the items indicated
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∑ₓ =
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the sum of all x-values
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∑ₓ² indicates:
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that each x-value should be squared and then those squares added.
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(∑ₓ)² indicates:
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that the x-values should be added and the total then squared.
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∑ₓᵧ indicates:
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that each x-value should first be multiplied by its corresponding y-value. After obtaining all such products, find their sum.
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r =
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the linear correlation coefficient for a sample of paired data.
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ρ =
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the linear correlation coefficient for a population of paired data.
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What are the requirements when making a conclusion about correlation in the population?
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1) The sample of paired (x,y) data is a simple random sample of quantitative data.
2) Visual examination of the scatterplot must confirm that the points approximate a straight-line pattern. 3) The pairs of (x,y) data must have a bivariate normal distribution. ( No outliers) |
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Conclude that "there is a strong linear correlation between x and y" if the P-value computed from r is:
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P-v ≤ α
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Conclude that "there is no linear correlation between x and y" if the P-value computed from r is:
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P-v > α
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x is the __________ or _____________ variable.
y is the __________ or _____________ variable. |
x is the Explanatory or Independent variable.
y is the Response or Dependent variable. |
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The value of r is always between:
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-1 and 1 That is,
-1 ≤ r ≤ 1 |
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If all values of either are converted to a different scale, does the value of r change?
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no, it doesn't change.
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Is the value of r affected by the choice of x or y? Meaning if you interchange all x and y values, will r change?
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No, interchange all x and y values and the value of r will not change.
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Does r measure the strength of a relationship that isn't linear?
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No, r measures the strength of a linear relationship. It is not designed to measure the strength of a relationship that is not linear.
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Is r sensitive to outliers?
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Yes, r is very sensitive to outliers in the sense that a single outlier can dramatically affect its value.
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The value of r² is the:
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proportion of the variation in y that is explained by the linear relationship between x and y.
If x is the cost of pizza and y the cost of fare, and r = 0.988 and r² = 0.976, then about 98% of the variation in the cost of a subway fare can be explained by the linear relationship between the costs of pizza and subway fares. This implies that about 2% of the variation in costs of subway fares cannot be explained by the costs of pizza. |
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What are the three common errors involving correlation?
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1) Concluding that correlation implies causality.
2) Calculating correlation based on avgs. (they can inflate correlation). 3) Thinking that because there is no LINEAR correlation, that there is no correlation at all. (There could be some other non-linear correlation.) |
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What is the procedure for hypothesis testing for correlation using the P-v method?
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1) Verify the requirements are met.
2) Find H₀ and Hₐ. 3) Find ttest. 4) Calculate P-v. (Use tcdf and n - 2 df) 5) Determine the relationship between P-v and α. 6) Make statement. |
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H₀: ρ = 0 means:
Hₐ: ρ ≠ 0 means: |
H₀: ρ = 0 means: No linear correlation between x and y.
Hₐ: ρ ≠ 0 means: There is a strong linear correlation between x and y. |
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For a claim of correlation,
H₀: Hₐ: |
H₀: ρ = 0 (oc)
Hₐ: ρ ≠ 0 (cc) |
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For a claim of a negative correlation,
H₀: Hₐ: |
H₀: ρ = 0 (cc)
Hₐ: ρ < 0 (oc) |
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For a claim of a positive correlation,
H₀: Hₐ: |
H₀: ρ = 0 (cc)
Hₐ: ρ > 0 (oc) |
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Conclude that "there is a strong linear correlation between x and y" if |rtest|:
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if the absolute value of rtest is greater than rcr. ie...
|rtest| > rcr. |
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Conclude that "there is no linear correlation between x and y" if|rtest|:
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if the absolute value of rtest is less than rcr. ie...
|rtest| ≤ rcr. |
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How do you use the TI-84 to find ∑ₓ, ∑ₓ², ∑ᵧ, ∑ᵧ², ∑ₓᵧ?
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TI-84 to find ∑ₓ, ∑ₓ², ∑ᵧ, ∑ᵧ², ∑ₓᵧ: stat, calc, 2-var stats, L₁,L₂
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How do you use the TI-84 to find the Ttest statistic and
P-v for the P-v method of hypothesis testing? |
stat, test, LinRegTTest, L₁, L₂
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How do you use the TI-84 to find r?
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stat, calc, LinReg(ax + b)
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n =
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the number of pairs of sample data
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What distribution is used when testing correlation?
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The Correlation Coefficient chart (table A - 6)
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df when testing correlation?
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There are no degrees of freedom. Use n (the number of pairs of sample data) to search for rcr on table A-6.
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What is the procedure for hypothesis testing for correlation using the rtest method?
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1) Verify the requirements are met.
2) Find H₀ and Hₐ. 3) Find rtest. 4) Find rcr. 5) Determine the relationship between rtest and rcr. 6) Make statement. |
