Natalie performs a chemistry experiment where she records the tenperture of an ongoing reaction.The solution is 93.5 C after 3 minutes;90 C after 5 minutes,84.8 C after 9 minutes; 70.2 C after 18 minute; 54.4 C after 30 minutes;42.5 C after 37 minutes; and 24.9 C after 48 minutes.Perform a linear regression on this data to complete the following items.

What does the value of the correlation coefficient tell you about correlation of the data?

Enter these data points into some graphing software, and ask the computer to perform a linear regression on the data (find the best-fit line that goes through the data points) The computer should also be able to calculate the correlation coefficient. If the correlation coefficient is 1, all the data points will lie along this line; The farther the correlation coefficient is from 1 and closer to 0 indicates that the points will be more scattered with respect to this line

To perform a linear regression on the given data, we need to plot the recorded temperatures against the corresponding time durations. This will allow us to visually assess the correlation between the temperature and time. We can then calculate the correlation coefficient, also known as Pearson's correlation coefficient, to understand the strength and direction of the relationship between these variables.

Step 1: Plotting the data

- On a graph, plot the time durations on the x-axis and the recorded temperatures on the y-axis.
- Mark the data points according to the given values: (3, 93.5), (5, 90), (9, 84.8), (18, 70.2), (30, 54.4), (37, 42.5), and (48, 24.9).
- Connect these points with a straight line to visualize the relationship between time and temperature.

Step 2: Calculating the correlation coefficient

- The correlation coefficient, denoted by r, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.
- To calculate r, we can use statistical software like Excel, Python, or specialized calculators. However, manual calculation requires multiple steps, including the mean, sum of squares, and covariance.
- For simplicity, let's assume you are using Excel:
- Enter the time durations in one column (A1 to A7) and the corresponding temperatures in another column (B1 to B7).
- Use the formula "=CORREL(B1:B7, A1:A7)" in a new cell to calculate the correlation coefficient.
- The result will be a value between -1 and +1. A positive value indicates a positive correlation, meaning as time increases, temperature also increases. A negative value indicates an inverse correlation, where as time increases, temperature decreases. A value close to 0 indicates a weak or no correlation.

Interpretation:

The resulting correlation coefficient will indicate the strength and direction of the relationship between time and temperature. If the value of the correlation coefficient is close to +1, it indicates a strong positive correlation, meaning that as time increases, temperature also increases significantly. If the value is close to -1, it indicates a strong negative correlation, meaning that as time increases, temperature decreases significantly. If the value is close to 0, it suggests a weak or no correlation, meaning there is no clear relationship between time and temperature in this dataset.

Therefore, calculating the correlation coefficient will help us determine the correlation of the data and understand the relationship between time and temperature in Natalie's chemistry experiment.