A. What decision should be made if a = .05? B. What is the line of best fit? C. Use the line of best fit to predict the y-variable if x = 2020
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Linear Regression T-Test Analysis
In the given image, a Linear Regression T-Test has been performed, and the results are displayed on a calculator screen. The relevant statistical outputs are as follows:
- **y = a + bx**: This is the equation of the regression line.
- **β ≠ 0 and p ≠ 0**: This indicates the hypothesis test results.
- **t = 5.32266509**: This is the t-statistic value.
- **p = 0.0017906207**: This is the p-value of the test.
- **df = 6**: Degrees of freedom.
- **a = -69662.13095**: The y-intercept of the regression line.
- **b = 34.98809524**: The slope of the regression line.
- **s = 42.60060455**: Standard error of the regression.
### Questions and Answers
#### A. What decision should be made if α = 0.05?
In hypothesis testing, the p-value is compared to the significance level (α) to determine whether to reject the null hypothesis. Here, the p-value is 0.0017906207, which is less than the significance level of 0.05.
**Decision:** Reject the null hypothesis (H0). This indicates that there is sufficient evidence to conclude that the slope of the regression line (β) is not equal to zero.
#### B. What is the line of best fit?
The line of best fit is represented by the regression equation derived from the test:
\[ y = a + bx \]
Given:
- \( a = -69662.13095 \)
- \( b = 34.98809524 \)
So, the line of best fit is:
\[ y = -69662.13095 + 34.98809524x \]
#### C. Use the line of best fit to predict the y-variable if x = 2020
To predict the y-variable for \( x = 2020 \):
\[ y = -69662.13095 + (34.98809524 \times 2020) \]
First, calculate the product:
\[ 34.98809524 \times 2020 = 70677.692688 \]
Then, add the y-intercept:
\[ y = -69662.13095 + 70677.692688](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41fb376d-216c-4c49-935b-f66a6cc42c2e%2F1574579a-7e0d-4bd3-b573-00de9926d83e%2F2zilc0n.jpeg&w=3840&q=75)
Step by step
Solved in 3 steps
