Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x = 102.69, y = 103.45, r= 0.912, P-value = 0.000, and y= -0.65+1.01x, where x represents the IQ score of the twin born first. Find the best predicted value of y given that the twin born first has an 1Q of 101? Use a significance level of 0.05.
Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x = 102.69, y = 103.45, r= 0.912, P-value = 0.000, and y= -0.65+1.01x, where x represents the IQ score of the twin born first. Find the best predicted value of y given that the twin born first has an 1Q of 101? Use a significance level of 0.05.
MATLAB: An Introduction with Applications
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![Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield \( \bar{x} = 102.69 \), \( \bar{y} = 103.45 \), \( r = 0.912 \), \( P\text{-value} = 0.000 \), and the regression equation is \( \hat{y} = -0.65 + 1.01x \), where \( x \) represents the IQ score of the twin born first. Find the best predicted value of \( y \) given that the twin born first has an IQ of 101. Use a significance level of 0.05.
Click the icon to view the critical values of the Pearson correlation coefficient \( r \).
The best predicted value of \( \hat{y} \) is [ ].
(Round to two decimal places as needed.)
\[ \text{Enter your answer in the answer box.} \]
---
This problem involves using linear regression to predict the IQ score of the second twin based on the IQ of the first twin. The regression equation given is used to make this prediction. The high correlation coefficient \( r = 0.912 \) signifies a strong positive relationship between the IQ scores of the twins. The P-value \( P = 0.000 \) indicates that this result is statistically significant at the 0.05 level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9d7df7e-1211-4d2e-80e0-69c049749f41%2F54a92c39-4843-41fd-8fa6-ba73dfab14b1%2F4xbslgo.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield \( \bar{x} = 102.69 \), \( \bar{y} = 103.45 \), \( r = 0.912 \), \( P\text{-value} = 0.000 \), and the regression equation is \( \hat{y} = -0.65 + 1.01x \), where \( x \) represents the IQ score of the twin born first. Find the best predicted value of \( y \) given that the twin born first has an IQ of 101. Use a significance level of 0.05.
Click the icon to view the critical values of the Pearson correlation coefficient \( r \).
The best predicted value of \( \hat{y} \) is [ ].
(Round to two decimal places as needed.)
\[ \text{Enter your answer in the answer box.} \]
---
This problem involves using linear regression to predict the IQ score of the second twin based on the IQ of the first twin. The regression equation given is used to make this prediction. The high correlation coefficient \( r = 0.912 \) signifies a strong positive relationship between the IQ scores of the twins. The P-value \( P = 0.000 \) indicates that this result is statistically significant at the 0.05 level.
Transcribed Image Text:Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
| x | 11 | 9 | 13 | 17 | 10 | 7 | 8 | 12 | 14 | 6 | 5 |
|----|----|----|----|----|----|----|----|----|----|----|----|
| y | 15.54 | 3.84 | 11.15 | 12.81 | 9.10 | 14.85 | 15.70 | 6.66 |
**(Round to two decimal places as needed.)**
Create a scatterplot of the data. Choose the correct graph below.
- **A.**
- Graph A displays points that form a curved pattern moving upwards then sharply downwards, resembling a quadratic trend.
- **B.**
- Graph B shows points scattered randomly around the plot with no discernible pattern or trend.
- **C.**
- Graph C features data points that follow a linear upward trend, clustered around a straight line.
- **D.**
- Graph D illustrates points forming a parabola-like curve, going upward and flaring outwards.
### Identify a characteristic of the data that is ignored by the regression line:
- **A.** There is an influential point that strongly affects the graph of the regression line.
- **B.** There is no trend in the data.
- **C.** The data has a pattern that is not a straight line.
- **D.** There is no characteristic of the data that is ignored by the regression line.
Click to select your answer(s).
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