Reference no: EM133266256
Sometimes we have data that can be paired together, such as height and weight of an individual. When two variables are measured and paired together, we have what we call paired data. When we have paired data, we can plot the results using a scatterplot. This will give us a visual to determine if there is a relationship between the variables of interest.
For two variable relationships, we can often report the data as ordered pairs in (x, y) format. Our x-variable in this case is known as the explanatory variable, and the y-variable is known as the response variable. We use values of x to predict y.
If there appears to be a linear relationship between the two variables, we can create a least squares regression line. This is a line that "best" fits the dataset we have. The result will be a linear equation and we can use this equation to predict future values.
For simple linear regression (ordered pairs with only two variables), the general form of a regression line follows:y^=β0+β1x, where β0 represents the intercept and β1represents the slope. We can now predict values of y for a given x-value.
Instructions
For this discussion post, we are going to linear regression model from a set of data. Suppose we get a job working for a company that provides their employees with company stock every year they work with the company. The amount of stock earned may be based on a few other variables, but all we are looking at right now is time served with the company. Here is the data we collected:
|
Years With Company
|
Company Stock (Thousands of $)
|
|
11
|
51
|
|
14
|
64
|
|
9
|
41
|
|
8
|
40
|
|
14
|
61
|
|
12
|
54
|
|
3
|
21
|
|
7
|
31
|
|
8
|
39
|
|
10
|
51
|
|
7
|
27
|
- Does the data look approximately linear? Or does there appear to be some sort of non-linear trend in our data?
- What is the regression model created from our data set?
- What does the slope represent in our regression model?
- If an employee has been with the company for 13 years, how much company stock would we expect them to have?
- In the problem, it was mentioned there are other variables that could impact the amount of company stock awarded to an employee. What are some other variables we may want to collect next time to add to our model?
- Make sure is clear formatting no pictures