Lesson

When we have bivariate data, we want to determine what sort of relationship the two variables have. As the independent variable ($x$`x`-axis) changes notice how the dependent variable ($y$`y`-axis) tends to change. Just by observation, we may notice the following:

**A simple relationship**: if the distribution of points appears to follow a trend either**linear**or**non-linear**depending on if the points appear to follow the shape of a line or not.

Consider being given an $x$`x`-value that doesn't correspond to any data point we have. Does the data set give us an idea of what $y$`y`-value that point should have to fit in with the rest of the data? If yes there might be a relationship. If not, there might be no relationship between the variables.

**Outliers**: in a scatterplot, any data points that are very different from the other data points will be quite obvious especially if the rest of the points appear to have a relationship.

Causal relationships

Even when two variables have a relationship, it may not be a **causal relationship**. We cannot say for sure that a change in the value of $x$`x` **causes** $y$`y` to change or that the value of $y$`y` **causes** a corresponding value of $x$`x` even when a relationship is apparent. It may be that both $x$`x` and $y$`y` have a relationship with some other hidden variable, which creates an indirect relationship between $x$`x` and $y$`y`.

The scatter plot shows the relationship between sea temperature and the amount of healthy coral.

Which variable is the dependent variable?

Sea temperature

ALevel of healthy coral

BSea temperature

ALevel of healthy coral

BWhich variable is the independent variable?

Sea temperature

ALevel of healthy coral

BSea temperature

ALevel of healthy coral

B

The scatterplot shows the height and weight of six students. Use the plot to answer the questions.

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How tall is the student who weighs $45$45kg?

How tall is the tallest student?

The price of ten houses is graphed against the house's land area below.

Describe the relationship between land area and house price in the data.

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As land area increases, house price decreases.

AAs land area increases, house price increases.

BLand area has no effect on house price.

CAs land area increases, house price decreases.

AAs land area increases, house price increases.

BLand area has no effect on house price.

C

Use scatter plots to investigate and comment on relationships between two numerical variables

Investigate and describe bivariate numerical data where the independent variable is time.