Question

Several bakeries in a town were asked the price for different amounts of donuts at their shop. A scatter plot with a line of best fit was created from the data gathered.

Part a: Estimate the correlation coefficient for the given data points.
a) 0.8
b) -0.6
c) 0.3
d) -0.1

Answer 1

To estimate the correlation coefficient, calculate the least-squares line and determine its strength and direction. Compare the calculated correlation coefficient to the given options.

Step-by-step explanation:

To estimate the correlation coefficient, we need to calculate the least-squares line and find the equation in the form y=a+bx. Then we can determine the correlation coefficient, which measures the strength and direction of the linear relationship between the variables. If the correlation coefficient is close to 1 or -1, it indicates a strong positive or negative correlation. If it's close to 0, the variables are not strongly related.

We can calculate the correlation coefficient using the equation r = √(b^2 / (b^2 + a^2)), where b is the slope and a is the y-intercept of the least-squares line. Once we have the correlation coefficient, we can determine its significance by comparing it to a critical value from a table or using a statistical calculator.

Given the options provided (0.8, -0.6, 0.3, -0.1), we cannot determine the exact correlation coefficient without the actual data points. However, we can estimate the correlation based on the options. A correlation coefficient of 0.8 indicates a strong positive correlation, -0.6 indicates a moderate negative correlation, 0.3 indicates a weak positive correlation, and -0.1 indicates a very weak negative correlation.