Question

1. in the linear regression equation y=mx + c, which of the following correctly describes each component? a) m indicates the value of y when x is zero, and c indicates the steepness of the line. b) m indicates the steepness of the line, and c indicates the value of y when x is zero. c) m represents the total distance between two points on the line, and c represents the horizontal line. d) m and c are interchangeable, and both represent the position of the line relative to the x - axis. 19. which of the following best describes the skewness of the distribution in the graph? a) symmetric b) left skewed c) right skewed d) cannot be determined from the histogram 20. a researcher is studying the number of hours of sleep participants get per night. after collecting data from 10 participants, the researcher finds the following values: 7,8,6,9,7,8,7,6,8,10. what is the mean hours of sleep? a) 7.6 b) 7.8 c) 8.6 d) 7.5

Explanation:

Step1: Recall linear - regression equation components

In the linear regression equation $y = mx + c$, $m$ is the slope which indicates the steepness of the line and $c$ is the y - intercept which is the value of $y$ when $x = 0$.

Step2: Analyze option for 18

Option B correctly describes $m$ as the steepness of the line and $c$ as the value of $y$ when $x$ is zero.

Step3: Analyze skewness for 19

In a right - skewed distribution, the tail of the distribution extends to the right. Looking at the histogram, the tail is on the right side, so it is right - skewed.

Step4: Calculate the mean for 20

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 10$ and $\sum_{i=1}^{10}x_{i}=7 + 8+6 + 9+7 + 8+7 + 6+8 + 10=76$. Then $\bar{x}=\frac{76}{10}=7.6$.

Answer:

1. B. $m$ indicates the steepness of the line, and $c$ indicates the value of $y$ when $x$ is zero.
2. C. right skewed
3. A. 7.6