Question

I want to see if there is a relation between makeup sales and the age of people buying them on any given day at Sephora. 10 people were randomly sampled.

X-axis: 13, 14, 16, 17, 21, 25, 30, 37, 50, 62 (age)

Y-axis: 2, 7, 30, 26, 15, 33, 7, 3, 14, 1 (Makeup sales)

What is the impact of using a linear regression model in this case? What options, other than linear regression, can you see? You do not need to collect any data.

For your response to a classmate (two responses required, one in each option), examine your classmate’s problem to assess the appropriateness and accuracy of using a linear regression model. Discuss the meaning of the standard error of the estimate and how it affects the predicted values of Y for that analysis.

Answer 1

Given:-

We have data of makeup sales and the age of people buying them on any given day at Sephora for the 10 people.

To do:-

1. Need to check the impact of using linear regression on this data

2. Is there any other technique we can use here?

3. Explain the meaning of Standard Error of the estimate and how it affects the predicted value of y.

Answers:-

1.Linear Regression using Excel Data Analysis.

Type the data>>Data>>Data Analysis>>Regression>>Select input output range>>OK

We can clearly stae that makeup sales is depending upon the age of customer.

Hence Makeup sales(y) is Dependent variable and age(x) is indepndent variable.

So We have to regress Y ~ X

Regression Output is attached here from this we can see that intercept (21.47241) and slope ( -0.269207 )

We can see that from p-value intercept is significant and slope is significant at 29.02 % which is not that much good.

As slope is negative it is clear that age is having negative impact on makeup sales.

Interpretation:- One year increase in age will cause 0.269207 decrease in the makeup scale

Note:- There may be some other variables which are responsible for the makeup sale since R2 and Adj.R2 are very less.

2. Alternative way to get some idea about the relationship is to study the correlation between those variables;

So we will calculate the correlation between age and makeup sales

corr(x,y) = -0.31173

i.e there is negative linear relationship between age and makeup sales

i.e makeup sales is less in the peoples with high age group and vice versa.

3.

Standard Error of the estimated coefficient is nothing but the accuracy measure of that estimate with respect to the corresponding population.It actually measures how far the sample estimate is far from population parameter.

Lower the standard error better is the prediction of the y. As standard error increases the prediced value becomes more un stable.