Math / Data & Statistics

QuestionWhich of the following statements about correlation is true?
Choose the correct answer below. A. We say that there is a negative correlation between $x$ and $y$ if the $x$ -values increase as the corresponding $y$ -values increase. B. We say that there is a positive correlation between $x$ and $y$ if the $x$ -values increase as the corresponding $y$ -values increase. C. We say that there is a positive correlation between $x$ and $y$ if there is no distinct pattern in the scatterplot. D. We say that there is a positive correlation between $x$ and $y$ if the $x$ -values increase as the corresponding $y$ -values decrease.

Studdy Solution

STEP 1

1. Correlation refers to the relationship between two variables, $x$ and $y$ .
2. Positive correlation implies that as one variable increases, the other variable also increases.
3. Negative correlation implies that as one variable increases, the other variable decreases.
4. No correlation implies no distinct pattern in the relationship between the variables.

STEP 2

1. Define positive correlation.
2. Define negative correlation.
3. Define no correlation.
4. Evaluate each statement against the definitions.

STEP 3

Define positive correlation: A positive correlation between $x$ and $y$ means that as the $x$ -values increase, the corresponding $y$ -values also increase.

STEP 4

Define negative correlation: A negative correlation between $x$ and $y$ means that as the $x$ -values increase, the corresponding $y$ -values decrease.

STEP 5

Define no correlation: No correlation means there is no distinct pattern in the scatterplot of $x$ and $y$ .

STEP 6

Evaluate each statement: - Statement A: Describes a negative correlation, which is incorrect for a negative correlation. - Statement B: Correctly describes a positive correlation. - Statement C: Describes no correlation, which is incorrect for a positive correlation. - Statement D: Describes a negative correlation, which is incorrect for a positive correlation.
The correct answer is:
$\boxed{\text{B}}$

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Studdy Solution

STEP 1

STEP 2

1. Define positive correlation.
2. Define negative correlation.
3. Define no correlation.
4. Evaluate each statement against the definitions.

STEP 3

Define positive correlation: A positive correlation between $x$ and $y$ means that as the $x$ -values increase, the corresponding $y$ -values also increase.

STEP 4

Define negative correlation: A negative correlation between $x$ and $y$ means that as the $x$ -values increase, the corresponding $y$ -values decrease.

STEP 5

Define no correlation: No correlation means there is no distinct pattern in the scatterplot of $x$ and $y$ .

STEP 6

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Studdy Solution

STEP 1

STEP 2

1. Define positive correlation.2. Define negative correlation.3. Define no correlation.4. Evaluate each statement against the definitions.

STEP 3

Define positive correlation: A positive correlation between x x x and y y y means that as the x x x-values increase, the corresponding y y y-values also increase.

STEP 4

Define negative correlation: A negative correlation between x x x and y y y means that as the x x x-values increase, the corresponding y y y-values decrease.

STEP 5

Define no correlation: No correlation means there is no distinct pattern in the scatterplot of x x x and y y y.

STEP 6

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1. Define positive correlation.
2. Define negative correlation.
3. Define no correlation.
4. Evaluate each statement against the definitions.

Define positive correlation: A positive correlation between $x$ and $y$ means that as the $x$ -values increase, the corresponding $y$ -values also increase.

Define negative correlation: A negative correlation between $x$ and $y$ means that as the $x$ -values increase, the corresponding $y$ -values decrease.

Define no correlation: No correlation means there is no distinct pattern in the scatterplot of $x$ and $y$ .