Math / Data & Statistics

QuestionHeights ( cm ) and weights ( kg ) are measured for 100 randomly selected adult males, and range from heights of 139 to 193 cm and weights of 38 to 150 kg . Let the predictor variable x be the first variable given. The 100 paired measurements yield $\bar{x}=167.54 \mathrm{~cm}, \bar{y}=81.44 \mathrm{~kg}, \mathrm{r}=0.185, P$ -value $=0.065$ , and $\hat{y}=-107+1.05 x$ . Find the best predicted value of $\hat{y}$ (weight) given an adult male who is 161 cm tall. Use a 0.05 significance level.
Click the icon to view the critical values of the Pearson correlation coefficient $r$ .
The best predicted value of $\hat{y}$ for an adult male who is 161 cm tall is $\square$ kg . (Round to two decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? If a dude is 161 cm tall, how heavy do we think he is, based on data from 100 other dudes? Watch out! The P-value is greater than the significance level, so the correlation isn't statistically significant.
This means our prediction might not be super reliable!

STEP 2

1. Check the significance
2. Make the prediction

STEP 3

Our P-value is $0.065$ , which is larger than our significance level of $0.05$ .

STEP 4

This means the correlation between height and weight isn't statistically significant.
So, using the regression equation might not be the best way to predict weight.

STEP 5

Even though the correlation isn't significant, the problem still wants us to use the equation.
We're given the equation $\hat{y} = -107 + 1.05x$ , where $x$ is the height.
We want to predict the weight $\hat{y}$ when $x = 161$ cm.
Let's plug it in: $\hat{y} = -107 + 1.05 \cdot 161$ .

STEP 6

$\hat{y} = -107 + 169.05$ .
So, $\hat{y} = 62.05$ .

STEP 7

The best predicted weight for a 161 cm tall adult male is 62.05 kg.

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Studdy Solution

STEP 1

What is this asking? If a dude is 161 cm tall, how heavy do we think he is, based on data from 100 other dudes? Watch out! The P-value is greater than the significance level, so the correlation isn't statistically significant.
This means our prediction might not be super reliable!

STEP 2

1. Check the significance
2. Make the prediction

STEP 3

Our P-value is $0.065$ , which is larger than our significance level of $0.05$ .

STEP 4

This means the correlation between height and weight isn't statistically significant.
So, using the regression equation might not be the best way to predict weight.

STEP 5

Even though the correlation isn't significant, the problem still wants us to use the equation.
We're given the equation $\hat{y} = -107 + 1.05x$ , where $x$ is the height.
We want to predict the weight $\hat{y}$ when $x = 161$ cm.
Let's plug it in: $\hat{y} = -107 + 1.05 \cdot 161$ .

STEP 6

$\hat{y} = -107 + 169.05$ .
So, $\hat{y} = 62.05$ .

STEP 7

The best predicted weight for a 161 cm tall adult male is 62.05 kg.

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Studdy Solution

STEP 1

What is this asking? If a dude is 161 cm tall, how heavy do we think he is, based on data from 100 other dudes? Watch out! The *P*-value is greater than the significance level, so the correlation isn't statistically significant.This means our prediction might not be super reliable!

STEP 2

1. Check the significance2. Make the prediction

STEP 3

Our *P*-value is 0.0650.0650.065, which is *larger* than our significance level of 0.050.050.05.

STEP 4

This means the correlation between height and weight isn't statistically significant.So, using the regression equation might not be the best way to predict weight.

STEP 5

STEP 6

y^=−107+169.05\hat{y} = -107 + 169.05y^​=−107+169.05.So, y^=62.05\hat{y} = 62.05y^​=62.05.

STEP 7

The best predicted weight for a 161 cm tall adult male is **62.05** kg.

Get Studdy

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.

What is this asking? If a dude is 161 cm tall, how heavy do we think he is, based on data from 100 other dudes? Watch out! The P-value is greater than the significance level, so the correlation isn't statistically significant.
This means our prediction might not be super reliable!

1. Check the significance
2. Make the prediction

Our P-value is $0.065$ , which is larger than our significance level of $0.05$ .

This means the correlation between height and weight isn't statistically significant.
So, using the regression equation might not be the best way to predict weight.

$\hat{y} = -107 + 169.05$ .
So, $\hat{y} = 62.05$ .

The best predicted weight for a 161 cm tall adult male is 62.05 kg.