Math / Data & Statistics

QuestionSuppose that you run a correlation and find the correlation coefficient is 0.325 and the regression equation is $\hat{y}=7.8 x-21.72$ . The centroid of your data was $(5.9,24.8)$ .
If the critical value is .632 , use the appropriate method to predict the $y$ value when $x$ is 3.9 $\square$

Studdy Solution

STEP 1

What is this asking? Given a regression equation, correlation coefficient, critical value, and centroid, predict the y-value for a specific x-value. Watch out! Don't forget to consider the critical value when deciding whether to use the regression equation or the mean y-value from the centroid for prediction!

STEP 2

1. Compare the correlation coefficient and the critical value.
2. Predict the y-value.

STEP 3

The absolute value of the correlation coefficient is $|0.325| = 0.325$ .
This tells us the strength of the linear relationship between x and y.

STEP 4

We're given a critical value of $0.632$ .
Since $0.325$ is less than $0.632$ , the correlation is not statistically significant.
This means we shouldn't use the regression equation for prediction!

STEP 5

Since the correlation isn't significant, the best prediction for any x-value is simply the average y-value, which is given by the y-coordinate of the centroid.
Our centroid is $(5.9, 24.8)$ , so the mean y-value is ** $24.8$ ‌.

STEP 6

Therefore, when $x = 3.9$ , our predicted y-value is $\hat{y} = 24.8$ .

STEP 7

The predicted y-value when $x = 3.9$ is $24.8$ .

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QuestionSuppose that you run a correlation and find the correlation coefficient is 0.325 and the regression equation is $\hat{y}=7.8 x-21.72$ . The centroid of your data was $(5.9,24.8)$ .
If the critical value is .632 , use the appropriate method to predict the $y$ value when $x$ is 3.9 $\square$

Studdy Solution

STEP 1

STEP 2

1. Compare the correlation coefficient and the critical value.
2. Predict the y-value.

STEP 3

The absolute value of the correlation coefficient is $|0.325| = 0.325$ .
This tells us the strength of the linear relationship between x and y.

STEP 4

We're given a critical value of $0.632$ .
Since $0.325$ is less than $0.632$ , the correlation is not statistically significant.
This means we shouldn't use the regression equation for prediction!

STEP 5

Since the correlation isn't significant, the best prediction for any x-value is simply the average y-value, which is given by the y-coordinate of the centroid.
Our centroid is $(5.9, 24.8)$ , so the mean y-value is ** $24.8$ ‌.

STEP 6

Therefore, when $x = 3.9$ , our predicted y-value is $\hat{y} = 24.8$ .

STEP 7

The predicted y-value when $x = 3.9$ is $24.8$ .

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Studdy Solution

STEP 1

STEP 2

1. Compare the correlation coefficient and the critical value.2. Predict the *y*-value.

STEP 3

The absolute value of the correlation coefficient is ∣0.325∣=0.325|0.325| = 0.325∣0.325∣=0.325.This tells us the strength of the linear relationship between *x* and *y*.

STEP 4

We're given a critical value of 0.6320.6320.632.Since 0.3250.3250.325 is less than 0.6320.6320.632, the correlation is *not* statistically significant.This means we shouldn't use the regression equation for prediction!

STEP 5

Since the correlation isn't significant, the best prediction for any *x*-value is simply the average *y*-value, which is given by the *y*-coordinate of the centroid.Our centroid is (5.9,24.8)(5.9, 24.8)(5.9,24.8), so the mean *y*-value is **24.824.824.8‌.

STEP 6

Therefore, when x=3.9x = 3.9x=3.9, our predicted *y*-value is y^=24.8\hat{y} = 24.8y^​=24.8.

STEP 7

The predicted *y*-value when x=3.9x = 3.9x=3.9 is 24.824.824.8.

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

1. Compare the correlation coefficient and the critical value.
2. Predict the y-value.

The absolute value of the correlation coefficient is $|0.325| = 0.325$ .
This tells us the strength of the linear relationship between x and y.

We're given a critical value of $0.632$ .
Since $0.325$ is less than $0.632$ , the correlation is not statistically significant.
This means we shouldn't use the regression equation for prediction!

Since the correlation isn't significant, the best prediction for any x-value is simply the average y-value, which is given by the y-coordinate of the centroid.
Our centroid is $(5.9, 24.8)$ , so the mean y-value is ** $24.8$ ‌.

Therefore, when $x = 3.9$ , our predicted y-value is $\hat{y} = 24.8$ .

The predicted y-value when $x = 3.9$ is $24.8$ .