Linear Data

Linear Data

​Scatterplots

We can visualize data involving two variables as scatterplots​

​

​A scatterplot is a graph of points, when we graph the data points we may be able to recognize a pattern.

​

​The scatterplot on the right appears to have a linear relationship.

​Correlation

Correlation is a measure of strength and direction of this relationship. Lets look at the direction.

​It is similar to slope. If the datapoints and graph is increasing, the correlation is positive. If the datapoints and graph is decreasing, the correlation is negative. At times the points appear neither decreasing or incresing overall. In this case there is no correlation

Multiple Choice

Describe the correlation of this scatterplot from the first slide.

• Positive

• Negative

• No correlation

Multiple Choice

Describe the correlation between the height of this tree and the years after planting. You can type the point into desmos if needed.

• Positive

• Negative

• No correlation

We can sometimes reasonable predict whether or not a situation has positive, negative, or no correlation without any data or graph.

​

​For example: the weight of a car and the number of miles per gallon

​ These two would probably have a negative correlation. This is beacuse a heavier car usually gets less miles to the gallon.

​

​For example: the amount of time studying and the grade on a science exam

​ These two would probably have a positive correlation. The more time a student puts into studying, the higher their grade will be

​

​ This is not always true, but it is a reasonable prediction.

Multiple Choice

Conside the number of dogs in a house and the amount of dog food needed.

• The number of dogs in a house and the amount of dog food needed is positively correlated.

• The number of dogs in a house and the amount of dog food needed isnegatively correlated.

• The number of dogs in a house and the amount of dog food needed has no correlation

Multiple Choice

The number of cars on the highway (the amount of traffic) and the cars’ average speed

• This data would probably have a positive correlation

• This data would probably have a negative correlation

• This data would probably have no correlation

​Correlation

​Now lets talk about correlation strength.

​

​We represent the strength of the correlation with a number between -1 and 1.

​

​The closer to 1 or -1, the stronger the correlation

Multiple Choice

Choose the BEST estimate for r, the correlation coefficient.

• 1

• -1

• -0.8

• 0.8

Multiple Choice

Estimate the correlation coefficient of this graph representing the relationship of scores between test 1 and test 2.

• -0.70

• 0.70

• -0.30

• 0.30

Multiple Choice

Can a correlation coefficient be 1.5?

• No, the correlation coefficeint must be between -1 and 1.

• Yes