Answer:
Explanation:
a) Scatter plot and Line of Best Fit:
To create a scatter plot, we plot the temperature on the x-axis (independent variable) and the number of seal failures on the y-axis (dependent variable).
Here are the data points:
Temperature (ºC): 16 5 9 12 7 10
Seal Failures: 3 12 8 6 4 7
Scatter plot:
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Temperature (ºC) | Seal Failures
--------------------------------
16 | 3
5 | 12
9 | 8
12 | 6
7 | 4
10 | 7
Now, let's draw the Line of Best Fit:
(Note: Since I cannot create a visual plot here, imagine a scatter plot with the points, and a straight line that best represents the general trend of the data.)
The Line of Best Fit is a straight line that represents the general trend of the data points. It is positioned in such a way that it minimizes the distance between the line and all the data points, showing the overall relationship between the variables.
Explanation of the trend:
The trend indicated by the Line of Best Fit will show whether there is a positive correlation (as temperature increases, seal failures increase) or a negative correlation (as temperature increases, seal failures decrease). The slope of the line indicates the direction and steepness of the trend, while the y-intercept represents the predicted value when the independent variable (temperature) is zero (although this might not make practical sense in this context).
b) Correlation coefficient and regression equation:
For calculating the correlation coefficient and the regression equation, you can use spreadsheet software like Microsoft Excel or graphing calculators like TI-84.
Explanation of correlation coefficient:
The correlation coefficient (usually denoted by 'r') measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1. A positive value of 'r' indicates a positive correlation, meaning as one variable increases, the other tends to increase as well. A negative value of 'r' indicates a negative correlation, meaning as one variable increases, the other tends to decrease. A value close to 0 indicates a weak or no linear relationship.
Explanation of regression equation:
The regression equation represents the line that best fits the data points and allows us to predict the dependent variable (seal failures) based on the independent variable (temperature). It is in the form of y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Without the actual data, I cannot calculate the correlation coefficient and regression equation. However, once you have the values, you can interpret them as follows:
Correlation coefficient (r): If the correlation coefficient is close to 1 or -1, it indicates a strong linear relationship between temperature and seal failures. If it is close to 0, it suggests a weak or no linear relationship.
Regression equation (y = mx + b): The slope (m) represents the change in seal failures per unit change in temperature. A positive slope indicates that as temperature increases, seal failures increase, and a negative slope indicates that as temperature increases, seal failures decrease. The y-intercept (b) represents the predicted number of seal failures when the temperature is 0, which might not have practical significance in this context.
To find the number of seal failures at a temperature of 140°C, you would simply plug in the temperature value (140) into the regression equation and solve for the corresponding seal failures value.