Math / Data & Statistics

Question $a_{1}{ }_{1}$ What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth? (1) 1.00 (3) -0.93 (2) 0.93 (4) -1.00

Studdy Solution

STEP 1

1. The data points are approximately: $(1, 8), (2, 7), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)$ .
2. The correlation coefficient measures the strength and direction of a linear relationship between two variables.
3. The correlation coefficient $r$ ranges from -1 to 1.

STEP 2

1. Analyze the trend of the data points.
2. Determine the direction and strength of the correlation.
3. Select the closest correlation coefficient from the given options.

STEP 3

Analyze the trend of the data points:
- The data points appear to decrease as the $x$ -values increase.

STEP 4

Determine the direction and strength of the correlation:
- The data points form a downward trend, indicating a negative correlation. - The points are closely aligned, suggesting a strong correlation.

STEP 5

Select the closest correlation coefficient from the given options:
- Given the negative and strong correlation, the closest option is $-0.93$ .
The correlation coefficient is:
$\boxed{-0.93}$

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Question $a_{1}{ }_{1}$ What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth? (1) 1.00 (3) -0.93 (2) 0.93 (4) -1.00

Studdy Solution

STEP 1

1. The data points are approximately: $(1, 8), (2, 7), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)$ .
2. The correlation coefficient measures the strength and direction of a linear relationship between two variables.
3. The correlation coefficient $r$ ranges from -1 to 1.

STEP 2

1. Analyze the trend of the data points.
2. Determine the direction and strength of the correlation.
3. Select the closest correlation coefficient from the given options.

STEP 3

Analyze the trend of the data points:
- The data points appear to decrease as the $x$ -values increase.

STEP 4

Determine the direction and strength of the correlation:
- The data points form a downward trend, indicating a negative correlation. - The points are closely aligned, suggesting a strong correlation.

STEP 5

Select the closest correlation coefficient from the given options:
- Given the negative and strong correlation, the closest option is $-0.93$ .
The correlation coefficient is:
$\boxed{-0.93}$

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Questiona11a_{1}{ }_{1}a1​1​ What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth? (1) 1.00 (3) -0.93 (2) 0.93 (4) -1.00

Studdy Solution

STEP 1

STEP 2

1. Analyze the trend of the data points.2. Determine the direction and strength of the correlation.3. Select the closest correlation coefficient from the given options.

STEP 3

Analyze the trend of the data points:- The data points appear to decrease as the x x x-values increase.

STEP 4

Determine the direction and strength of the correlation:- The data points form a downward trend, indicating a negative correlation. - The points are closely aligned, suggesting a strong correlation.

STEP 5

Select the closest correlation coefficient from the given options:- Given the negative and strong correlation, the closest option is −0.93-0.93−0.93. The correlation coefficient is:−0.93 \boxed{-0.93} −0.93​

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $a_{1}{ }_{1}$ What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth? (1) 1.00 (3) -0.93 (2) 0.93 (4) -1.00

1. Analyze the trend of the data points.
2. Determine the direction and strength of the correlation.
3. Select the closest correlation coefficient from the given options.

Analyze the trend of the data points:
- The data points appear to decrease as the $x$ -values increase.

Determine the direction and strength of the correlation:
- The data points form a downward trend, indicating a negative correlation. - The points are closely aligned, suggesting a strong correlation.

Select the closest correlation coefficient from the given options:
- Given the negative and strong correlation, the closest option is $-0.93$ .
The correlation coefficient is:
$\boxed{-0.93}$