## Envision Math Grade 8 Volume 1 Chapter 4 Investigate Bivariate Data

**Page 217 Exercise 1 Answer**

It is given that Angus has a big test coming up.

We have to make a general statement about which option leads to a better result.

The data regarding Angus is given, where it is given that in different test at what time he sleeps and when he gets up.

On observing the given data, we can observe that in the test 6, Angus goes to bed at 9pm which is early and, in that test, he scores the highest marks and the best result.

Therefore, the better option which will lead to a better result is that he should go to bed early for the best results in the test.

The better option which will lead to a better result is that he should go to bed early for the best results in the test.

**Page 217 Exercise 1 Answer**

We need to find the other factors should Angus take into consideration to make a decision.

The Correlation coefficient is a statistical calculation that is used to examine the relationship between two sets of data.

If we look closely at the test and their result, we can see that when he goes to bed early then Angus has the best results. The results differ by only a little but still the results are better when he goes to bed early.

The results are better when he goes to bed early.

The results are better when he goes to bed early.

**Page 218 Question 1 Answer**

We need to explain how we can describe the association of two data sets.

The Correlation coefficient is a statistical calculation that is used to examine the relationship between two sets of data.

We describe the relationship between the two sets of data with associations.

We can use the scatter plot for given relationship to determine whether there is strong, weak or no association.

We describe it with association.

We describe the relationship between the two sets of data with associations.

We can use the scatter plot for given relationship to determine whether there is strong, weak or no association.

**Page 218 Exercise 1 Answer**

To find – The relationship might there be between the two measurements

Correlation coefficient values can range between +1.00 to -1.00.

The Correlation coefficient is a statistical calculation that is used to examine the relationship between two sets of data.

The value of the correlation coefficient tells us about the strength and the nature of the relationship.

Correlation coefficient values can range between +1.00 to -1.00.

Statistical measures which show a relationship between two or more variable or two or more sets of data. For example, generally there is a high relationship or correlation between parent’s education and academic achievement.

Statistical measures which show a relationship between two or more variable or two or more sets of data. For example, generally there is a high relationship or correlation between parent’s education and academic achievement.

**Page 218 Exercise 1 Answer**

Given that, Georgia and her classmates also measure their foot length. Use a pencil to find the trend line. We need to sketch the trend line for the scatter plot.

Simply place the pencil on the scatter plot so it goes right through the middle of all point and then sketch line.

Place the pencil on the scatter plot so it goes right through the middle of all points and then sketch that line.

Place the pencil on the scatter plot so it goes right through the middle of all points and then sketch that line.

**Page 219 Exercise 2 Answer**

To find the association between the data.

Place the pencil on the scatter plot so it goes right through the middle of all points.

If the points are all close to the pencil, than the association is strong.

If the points are all scattered around and not close to the pencil, that the association is weak.

If the points are not close to the pencil, and do not have any pattern, than there is no association.

Given graph has strong association.

To find the association between the data.

Place the pencil on the scatter plot so it goes right through the middle of all points.

If the points are all close to the pencil, than the association is strong.

If the points are all scattered around and not close to the pencil, that the association is weak.

If the points are not close to the pencil, and do not have any pattern, than there is no association.

Given graph has weak association.

To find the association between the data.

Place the pencil on the scatter plot so it goes right through the middle of all points.

If the points are all close to the pencil, than the association is strong.

If the points are all scattered around and not close to the pencil, that the association is weak.

If the points are not close to the pencil, and do not have any pattern, than there is no association.

Given graph has no association.

**Page 220 Exercise 1 Answer**

We need to explain how we can describe the relationship between the two sets of data.

The value of the correlation coefficient tells us about the strength and the nature of the relationship.

Correlation coefficient values can range between +1.00 to -1.00.

The relationship between the two sets of data is described using associations.

We can determine whether the two sets of data are having strong, weak, or have no associations between them.

Associations describe the relationship between the two sets of data.

Using a scatter plot, we can determine whether the given two sets of data is having strong, weak, or no association.

**Page 220 Exercise 2 Answer**

Given- a trend line

To find- How does a trend line describe the strength of the association?

If the points are close to the trend line then the association is strong

Place the pencil on the scatter plot so it goes right through the middle of all points.

If the points are all close to the pencil, than the association is strong.

If the points are all scattered around and not close to the pencil, that the association is weak.

If the points are not close to the pencil, and do not have any pattern, than there is no association

We use the pencil to find the trend line. If the points are close to the trend line then the association is strong, if they are scattered around but not so close to the pencil, then the association is weak and if the points are scattered all around the graph, then there is no association.

We use the pencil to find the trend line. If the points are close to the trend line then the association is strong, if they are scattered around but not so close to the pencil, then the association is weak and if the points are scattered all around the graph, then there is no association.

**Page 220 Exercise 5 Answer**

To find- The association between the data.

The value of the correlation coefficient tells us about the strength and the nature of the relationship.

Place the pencil on the scatter plot so it goes right through the middle of all points.

If the points are all close to the pencil then the association is strong.

If the points are all scattered around and not close to the pencil, that the association is weak.

If the points are not close to the pencil and do not have any pattern then there is no association.

Given graph has no association.

**Page 221 Exercise 6 Answer**

Given

To find/solve

Best model of the data

If we look closely at the lines on the graph, then we can see that the line that we need is m.

All of the points are more close to line m than any other line.

Hence the best model is the line m.

All of the points are more close to line m than any other line.

Hence the best model is the line m.

**Page 221 Exercise 8 Answer**

To find- Positive or negative linear association.

A positive correlation is a relationship between two variables that move in tandem—that is, in the same direction.

Since we have the time working and the amount of money earned, then we know that the graph is going to be positive meaning that the more time working we have, the more money we are going to earn.

This is going to be a positive association.

This is going to be a positive association.

**Page 221 Exercise 9 Answer**

Given

To find/solve

Relationship between the data .

As we can see on the graph the trend line is going to be descending which means that the association is going to be negative.

If we draw the trend line with pencil, then we can see the association is strong negative.

On the given graph we can see strong negative association.

If we draw the trend line with pencil, then we can see the association is strong negative.

On the given graph we can see strong negative association.

**Page 222 Exercise 13 Answer**

Given- scatter plot showing a linear relationship.

To find- if a scatter plot shows a linear relationship

The y-values change with respect to the x-values at a constant rate. This means that the points are going to be forming a line.

The y-values change with respect to the x-values at a constant rate.

The y-vales change with respect to thex-values at a constant rate. This means that the points are going to be forming a line.

The y-values change with respect to the x-values at a constant rate.