Answer :
Based on the scatter diagram, the most likely r value is option iii) -0.5, as the data points show a scattered pattern with no clear linear trend.
a) Drawing a line of best fit involves finding a line that best represents the trend or pattern in the scatter diagram. This line should minimize the distance between the line and the data points. The line can be drawn by eye or using regression techniques such as linear regression. The line should reflect the overall trend of the data points.
b) The relationship between the number of siblings and salary can be inferred by observing the scatter diagram. If the line of best fit has a positive slope, it suggests a positive relationship, indicating that as the number of siblings increases, the salary tends to increase. Conversely, if the line of best fit has a negative slope, it suggests a negative relationship, indicating that as the number of siblings increases, the salary tends to decrease.
c) Looking at the scatter diagram, we can assess the likely value of the correlation coefficient (r) based on the pattern of the data points.
If the data points align closely to a perfectly straight line with a positive slope, indicating a strong positive relationship, an r value of 0.8 is most likely.
If the data points align closely to a perfectly straight line with a negative slope, indicating a strong negative relationship, an r value of -0.8 is most likely.
If the data points are scattered and show no clear pattern or linear trend, an r value close to 0 or around -0.5 would be more likely.
Ultimately, the most likely r value depends on the specific arrangement and pattern of the data points in the scatter diagram.
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