Question

1 A scatter diagram of data collected in a study using love of music is being predicted by hearing sensitivity. A dot located at 4.5 across and 8 up means the person had a score of 4.5 on?

2)A scatter diagram in which the dots form a kind of upside-down “U” shape is an example of a(n) __________ correlation.?

3)In a perfect linear correlation, the dots in a scatter diagram all fall ___

Answer 1

In this scenario we have to investigate the relationship between the love of music and hearing sensitivity.

To investigate association between two variables first step is to make scatter plot i.e we have visual idea about the association between two variables.

1)2)A scatter diagram in which the dots form a kind of upside-down “U” shape is an example of a non linear correlation.

The example of U shaped scatter plot is given below,

Notice that from the above scatter plot out data is not linear that menas first at high value of y there is low value of x Variable and then the pattern is changed after some point the y increases x is also increased i.e the data is non-linear .

If the data is not linear the slope of Regression line is continuously changes. If our data is linear then slope will not change. The example of perfect positive correlation is given below.

3)In a perfect linear correlation, the dots in a scatter diagram all fall in straight line.

The example of perfect linear correlation is given below,

here from the above scatter plot notice that the data is perfectly in linear trend that means as y values increases x values also increases .

Here also note that the slope is fixed it is not changed. So the regression model is appropriate to use in this scenario.

Hope it helps.

Thank you.