For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x = 6.2, y = 6.0, r=-0.209, P-value = 0.144, and y=7.48-0.239x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=4. Use a 0.05 significance level. The best predicted value of y when x=4 is 6.5 (Round to one decimal place as needed.)
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x = 6.2, y = 6.0, r=-0.209, P-value = 0.144, and y=7.48-0.239x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=4. Use a 0.05 significance level. The best predicted value of y when x=4 is 6.5 (Round to one decimal place as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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![**Educational Website Content**
### Analysis of Attractiveness Ratings in Speed Dating Context
In a study involving 50 randomly selected speed dates, attractiveness ratings were compiled. Males rated their female date partners on a scale of 1 to 10 (x), and females rated their male date partners on the same scale (y).
Key statistics obtained from the 50 paired ratings include:
- Mean attractiveness rating by males (\(\bar{x}\)) = 6.2
- Mean attractiveness rating by females (\(\bar{y}\)) = 6.0
- Correlation coefficient (r) = -0.209
- P-value = 0.144
Using linear regression analysis, the equation for predicting the female's rating of a male is given by:
\[ \hat{y} = 7.48 - 0.239x \]
**Objective:**
To find the best-predicted value of \(\hat{y}\) (attractiveness rating by females of males) for a date in which the male's attractiveness rating by the female is \(x = 4\).
**Calculation:**
Substitute \(x = 4\) into the regression equation:
\[ \hat{y} = 7.48 - 0.239(4) \]
\[ \hat{y} = 7.48 - 0.956 \]
\[ \hat{y} = 6.5 \]
Thus, the best-predicted value of \(\hat{y}\) when \(x = 4\) is **6.5** (rounded to one decimal place as required).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F552c0758-5203-44a0-803c-786f9a348f99%2Fecf40bcf-5215-40e3-b63e-7f04ea741ee3%2Fy38iub_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Content**
### Analysis of Attractiveness Ratings in Speed Dating Context
In a study involving 50 randomly selected speed dates, attractiveness ratings were compiled. Males rated their female date partners on a scale of 1 to 10 (x), and females rated their male date partners on the same scale (y).
Key statistics obtained from the 50 paired ratings include:
- Mean attractiveness rating by males (\(\bar{x}\)) = 6.2
- Mean attractiveness rating by females (\(\bar{y}\)) = 6.0
- Correlation coefficient (r) = -0.209
- P-value = 0.144
Using linear regression analysis, the equation for predicting the female's rating of a male is given by:
\[ \hat{y} = 7.48 - 0.239x \]
**Objective:**
To find the best-predicted value of \(\hat{y}\) (attractiveness rating by females of males) for a date in which the male's attractiveness rating by the female is \(x = 4\).
**Calculation:**
Substitute \(x = 4\) into the regression equation:
\[ \hat{y} = 7.48 - 0.239(4) \]
\[ \hat{y} = 7.48 - 0.956 \]
\[ \hat{y} = 6.5 \]
Thus, the best-predicted value of \(\hat{y}\) when \(x = 4\) is **6.5** (rounded to one decimal place as required).
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