# Interpreting diagrams for SQA National 5 Maths

1. Line of best fit

The line of best fit is a straight line drawn through as many scatter points as possible. Its gradient should generally follow the same steepness of the scatter points. The line of best fit can then be used to make predictions about the values of the variables.

# 1

The line of best fit between the number of hours spent studying by a student in a week and their percentage grade is given by the equation y = 4x + 18. Explain what this says about the correlation between the two variables.

The positive gradient of the line of best fit means that the two variables are positively correlated. The gradient of 4 means that for every unit increase in the number of hours spent studying by the student, their grade increases by 4%. The y-inctercept means that a student that does no studying in a week will get a grade of 18%.

# 2

Sketch a scatter plot for two positively correlated variables and draw the line of best fit through the scatter plot.

image

# 3

Find the equation of the line of best fit between the age of a person and the average number of words used in a sentence, given that a 15 year old is found to use 11 words on average.

Given that a baby speaks 0 words, the gradient is calculated using gradient = 11/15. Since the line goes through the origin, the equation of the line of best fit is given by y = (11/15)x.

# 4

Given that the line of best fit through a set of scatter points is very steep and negatively sloped, describe the correlation between the two variables.

The scatter points must follow the steepness of the line of best fit. Thus, it can be deduced that the two variables are strongly negatively correlated, since the gradient of the line of best is very negative.

# 5

A scatter plot between the temperature in ˚C and the number of people at the beach on a day is plotted and the line of best fit is found to have the equation y = 10x. Explain what this means about the relationship between the two variables.

The positive gradient of the line of best fit means that the two variables are positively correlated. The gradient of 10 means that for every unit increase in the temperature, 10 more people go to the beach. The y-intercept is 0, meaning that when the temperature is 0 ˚C, there are no people at the beach.

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