Question

The table shows the amount Andre earned as a waiter. The money, in dollars, is the total amount he earned.

Times (hours) 0, 1, 2, 3, 4, 5, 6, 7
Money (dollars) 0, 16, 35, 47, 60, 69, 90, 103

Let a represent the number of hours. Write a linear regression equation for the data. Round the slope and y-intercept to the nearest whole number.
Find the correlation coefficient, or r-value, of the line. Explain what does this indicate.

Answer 1

The linear regression equation for the given data is y = 13x + 16, and the correlation coefficient (r-value) is approximately 0.976.

Step-by-step explanation:

The linear regression equation y = 13x + 16 represents the relationship between the number of hours worked (x) and the total earnings (y) for Andre as a waiter. The slope, rounded to the nearest whole number, is 13, indicating that for every additional hour worked, Andre earns approximately $13 more. The y-intercept, rounded to the nearest whole number, is 16, suggesting that even at zero hours worked, there's a base earning of $16.

The correlation coefficient (r-value) of approximately 0.976 indicates a strong positive linear relationship between the hours worked and the earnings. This value is close to 1, signifying a high degree of correlation where an increase in hours worked consistently corresponds to an increase in earnings. Therefore, the model fits the data well and can be used to predict Andre's earnings based on the hours he works.

Understanding this linear relationship is crucial for Andre to estimate his potential earnings based on the hours he intends to work, offering insight into his expected income and helping him make informed decisions about his work schedule.