Math / Data & Statistics

QuestionMatch these values of $r$ with the accompanying scatterplots: $1$ , $0.412$ , $-0.753$ , $0.998$ , and $1$ . Click the icon to view the scatterplots. Match the values of $r$ to the scatterplots. Scatterplot 1, $r =$ Scatterplot 2, $r =$ Scatterplot 3, $r =$ Scatterplot 4, $r =$ Scatterplot 5, $r =$ Scatterplots

Studdy Solution

STEP 1

What is this asking? We need to match each scatterplot with its correlation coefficient $r$ , which tells us how strongly the data points follow a straight line. Watch out! A positive $r$ means an upward trend, a negative $r$ means a downward trend, and the closer $r$ is to $|1|$ , the tighter the points cluster around a line.

STEP 2

1. Perfect Correlations
2. Strong Positive Correlation
3. Moderate Positive Correlation
4. Weak Positive Correlation
5. Moderate Negative Correlation

STEP 3

Scatterplot 3 shows a perfect positive correlation.
As $x$ increases, $y$ increases perfectly consistently.
This means $r = \mathbf{1}$ .

STEP 4

There's no perfectly negative correlation, so we've found our first match!

STEP 5

Scatterplot 5 shows a strong positive correlation.
The points in Scatterplot 5 are very close to forming a straight, upward-sloping line.
This suggests a high positive $r$ value.

STEP 6

The value $\mathbf{r = 0.998}$ is the strongest positive correlation available, so it must belong to Scatterplot 5.

STEP 7

Scatterplot 2 shows a moderate positive correlation.
The points generally trend upwards, but with more scatter than Scatterplot 5.

STEP 8

The remaining positive $r$ values are $0.412$ and $0.753$ .
Since the correlation in Scatterplot 2 is more noticeable than Scatterplot 4, the value $\mathbf{r = 0.753}$ fits Scatterplot 2.

STEP 9

Scatterplot 4 shows a weak positive correlation.
The points are quite scattered, but there's still a slight upward trend.

STEP 10

The only remaining positive $r$ value is $\mathbf{0.412}$ , so it matches Scatterplot 4.

STEP 11

Scatterplot 1 shows a moderate negative correlation.
As $x$ increases, $y$ generally decreases, but with some scatter.

STEP 12

The only remaining $r$ value is $\mathbf{-0.753}$ , which makes sense for the moderately negative correlation in Scatterplot 1.

STEP 13

Scatterplot 1: $r = -0.753$ Scatterplot 2: $r = 0.753$ Scatterplot 3: $r = 1$ Scatterplot 4: $r = 0.412$ Scatterplot 5: $r = 0.998$

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Studdy Solution

STEP 1

STEP 2

1. Perfect Correlations
2. Strong Positive Correlation
3. Moderate Positive Correlation
4. Weak Positive Correlation
5. Moderate Negative Correlation

STEP 3

Scatterplot 3 shows a perfect positive correlation.
As $x$ increases, $y$ increases perfectly consistently.
This means $r = \mathbf{1}$ .

STEP 4

There's no perfectly negative correlation, so we've found our first match!

STEP 5

Scatterplot 5 shows a strong positive correlation.
The points in Scatterplot 5 are very close to forming a straight, upward-sloping line.
This suggests a high positive $r$ value.

STEP 6

The value $\mathbf{r = 0.998}$ is the strongest positive correlation available, so it must belong to Scatterplot 5.

STEP 7

Scatterplot 2 shows a moderate positive correlation.
The points generally trend upwards, but with more scatter than Scatterplot 5.

STEP 8

The remaining positive $r$ values are $0.412$ and $0.753$ .
Since the correlation in Scatterplot 2 is more noticeable than Scatterplot 4, the value $\mathbf{r = 0.753}$ fits Scatterplot 2.

STEP 9

Scatterplot 4 shows a weak positive correlation.
The points are quite scattered, but there's still a slight upward trend.

STEP 10

The only remaining positive $r$ value is $\mathbf{0.412}$ , so it matches Scatterplot 4.

STEP 11

Scatterplot 1 shows a moderate negative correlation.
As $x$ increases, $y$ generally decreases, but with some scatter.

STEP 12

The only remaining $r$ value is $\mathbf{-0.753}$ , which makes sense for the moderately negative correlation in Scatterplot 1.

STEP 13

Scatterplot 1: $r = -0.753$ Scatterplot 2: $r = 0.753$ Scatterplot 3: $r = 1$ Scatterplot 4: $r = 0.412$ Scatterplot 5: $r = 0.998$

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Studdy Solution

STEP 1

STEP 2

1. Perfect Correlations2. Strong Positive Correlation3. Moderate Positive Correlation4. Weak Positive Correlation5. Moderate Negative Correlation

STEP 3

Scatterplot 3 shows a perfect positive correlation.As xxx increases, yyy increases perfectly consistently.This means r=1r = \mathbf{1}r=1.

STEP 4

There's no perfectly negative correlation, so we've found our first match!

STEP 5

Scatterplot 5 shows a strong positive correlation.The points in Scatterplot 5 are very close to forming a straight, upward-sloping line.This suggests a high positive rrr value.

STEP 6

The value r=0.998\mathbf{r = 0.998}r=0.998 is the strongest positive correlation available, so it must belong to Scatterplot 5.

STEP 7

Scatterplot 2 shows a moderate positive correlation.The points generally trend upwards, but with more scatter than Scatterplot 5.

STEP 8

The remaining positive rrr values are 0.4120.4120.412 and 0.7530.7530.753.Since the correlation in Scatterplot 2 is more noticeable than Scatterplot 4, the value r=0.753\mathbf{r = 0.753}r=0.753 fits Scatterplot 2.

STEP 9

Scatterplot 4 shows a weak positive correlation.The points are quite scattered, but there's still a slight upward trend.

STEP 10

The only remaining positive rrr value is 0.412\mathbf{0.412}0.412, so it matches Scatterplot 4.

STEP 11

Scatterplot 1 shows a moderate negative correlation.As xxx increases, yyy generally decreases, but with some scatter.

STEP 12

The only remaining rrr value is −0.753\mathbf{-0.753}−0.753, which makes sense for the moderately negative correlation in Scatterplot 1.

STEP 13

Scatterplot 1: r=−0.753r = -0.753r=−0.753 Scatterplot 2: r=0.753r = 0.753r=0.753 Scatterplot 3: r=1r = 1r=1 Scatterplot 4: r=0.412r = 0.412r=0.412 Scatterplot 5: r=0.998r = 0.998r=0.998

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1. Perfect Correlations
2. Strong Positive Correlation
3. Moderate Positive Correlation
4. Weak Positive Correlation
5. Moderate Negative Correlation

Scatterplot 3 shows a perfect positive correlation.
As $x$ increases, $y$ increases perfectly consistently.
This means $r = \mathbf{1}$ .

Scatterplot 5 shows a strong positive correlation.
The points in Scatterplot 5 are very close to forming a straight, upward-sloping line.
This suggests a high positive $r$ value.

The value $\mathbf{r = 0.998}$ is the strongest positive correlation available, so it must belong to Scatterplot 5.

Scatterplot 2 shows a moderate positive correlation.
The points generally trend upwards, but with more scatter than Scatterplot 5.

The remaining positive $r$ values are $0.412$ and $0.753$ .
Since the correlation in Scatterplot 2 is more noticeable than Scatterplot 4, the value $\mathbf{r = 0.753}$ fits Scatterplot 2.

Scatterplot 4 shows a weak positive correlation.
The points are quite scattered, but there's still a slight upward trend.

The only remaining positive $r$ value is $\mathbf{0.412}$ , so it matches Scatterplot 4.

Scatterplot 1 shows a moderate negative correlation.
As $x$ increases, $y$ generally decreases, but with some scatter.

The only remaining $r$ value is $\mathbf{-0.753}$ , which makes sense for the moderately negative correlation in Scatterplot 1.

Scatterplot 1: $r = -0.753$ Scatterplot 2: $r = 0.753$ Scatterplot 3: $r = 1$ Scatterplot 4: $r = 0.412$ Scatterplot 5: $r = 0.998$