Question

In SAS: Create a scatterplot of MaxSalary versus Score from the dataset found at the link below.

'salarygov' found here: https://drive.google.com/file/d/1JKwW0byCWK54OPpNdSiOmYkACMbdyClo/view?usp=sharing

Question 1 options (Select all that apply):

The scatterplot shows underlying group effects existing.
The scatterplot appears curved.
The scatterplot appears to have differing levels of variation depending on the value of score.
Simple linear regression is an appropriate choice for this data based on the scatterplot.

Could you post the code that you used and/or the steps used to generate this through tasks and utilities?

Answer 1

1. Scatter Plot of Y and X1

Scatter plot of sales and calls shows that there can be a linear trend between the both. The trendline indicates that it looks like higher the number of calls, higher will be sales

2. Best fit line

Using the Regression option in Excel Data analysis menu, we obtaain the following output

From this, bestfit line equation is Sales=Intercept+Coefficient of Calls *Calls

i.e., Sales = 22.52 + 0.1237 * Calls

3. Coefficient of Correlation

It denotes the strength of association between two variables. The sign denotes the direction of association.

In Exel, we calculate Correlation coefficient as Correl(X1array,Yarray)

We get the value as 0.318

This means that calls and sales are slightly positively associated. With increase in one quantiity, the other is also showing an increasing trend. Please note that this does not imply causation, i.e.,we CANNOT say that the rise or fall in one is causing the change in other.

4. Coefficient of Determination

It is more commonly known as R squared value. It gives the measure of how close the data points are to the best fit line. In other words, it gives the proportion of variability in dependent variable that can be explained by the independent variable. Higher the Rsquared value, better the model is.

From Excel regression output, we get R squared value or Coefficient of Determination as 0.101

~10% of variability in sales is explained by calls.

5. Utility of Regression model

F test can be used to test the utility of the model.

Null Hypothesis: Beta coefficient of call = 0; i.e., Calls is NOT linearly associated with sales

Alternate Hypothesis: Beta coefficient of call 0; Calls is linearly associated with sales

Let us choose significance level, = 0.05.

From the regression ANOVA output, we get p value (or significance value) of F test as 0.0012 (<0.05) for the given degrees of freedom (highlighted)

Since p value < , we can reject Null hypothesis, thereby concluding that with the given data it can be said that calls is linearly associated with sales.

6. Based on the above findings, it can be said that calls is a good and important variable in predicting sales volume. It has been proved that calls and sales have a positive linear association between them. From the best fit line (Sales = 22.52 + 0.1237 * Calls), we can say that with every call, sales increases by 0.1237units (interpretation of coefficient of calls).

7. 95% Confidence Interval

The 95% confidence interval for the coefficient of Calls (1) is [0.0498, 0.1976]

Interpretation: 95% confidence interval means that if this regression analysis is to be repeated for other samples from population, 95% of the intervals will contain the true value of 1. In simpler terms, we can say that we are 95% confident that the true value of 1 is in our interval.

8. Sales = 22.52 + 0.1237 * Calls

Let us say calls = 100.

95% confidence interval for 1 = [0.0498, 0.1976]

Thus, lower limit of Sales value, Y_low = 22.52 + 0.0498 * 100 = 27.5

Upper limit of Sales value, Yhigh = 22.52 + 0.1976 * 100 = 42.28

Thus, for calls = 100, Sales can be expected to be in the range of [27.5, 42.28]