We can measure the association between two numeric variables as a correlation. If larger than average values of one variable are associated with smaller than average values of the other variable then this would be a negative correlation. Correlations range between -1 and 1 and we can test the signiicance of a correlation using a t test statistic.

A regression is used when we want to predict how one numeric variable (response variable) will change in response to changes in some other numeric variable (predictor).

Regressions allow us to make predictions about what value we expect to see in our response variable for a given value in our predictor variable. We can also measure how different our observed values were from our predicted (fitted) values (i.e. residuals). This video also explains how we can assess the assumptions of regression.

1. I plant 40 seedlings and give them various exposure to light (measure in lux). After a month, I measure each seedling to check its growth. I want to know if there is a relationship between the amount of light each plant received, and the amount it has grown. In this example, light measured in lux is the:

   (A) explanatory variable, or

   (B) response variable?

2. Which of the following assumptions do we make while deriving linear regression parameters? (More than one may be true)

   (A) The true relationship between the response y and predictor x is linear.
   (B) The model errors are independent.
   (C) The errors are normally distributed with a 0 mean and constant standard deviation.
   (D) The predictor x is non-stochastic (constant) and is measured error-free.

3. What does a negative correlation coefficient indicate?