In an effort to control costs associated inventory

Question

Regression Analysis

Project #1 - Simple Linear Regression

Data: SLR.xls

In an effort to control costs associated inventory management, a study was conducted on the relationship between sales (X, in billions of US dollars) and inventory levels (Y, in billions of US dollars), with a random sample of size 20. You are assigned to develop a simple linear regression model and report the results.

Assignment:

1. Compute the descriptive statistics for both Y and X, including (but not limited to):

n, mean, median, std, min and max.

2. Show the scatterplot between Y and X. Is a linear model appropriate for the data?

3. Compute the Pearson and Spearman correlations between Y and X and test the null hypothesis of ρ = 0.

4. Suppose the regression model is Y = β0 + β1 X + e, fit the model to the SLR data. Show the regression equation and interpret the meaning of the two coefficients.

5. What is the R2 of the model? What is the meaning of the R2.

6. Are both coefficients significant? Interpret the 95% CI for the two coefficients.

7. What is the predicted value of Y if X = 250 and 300.

Answer 1

For the given simple linear regression problem, developing model and reporting the results are main concern. In an effort to control costs related inventory management, a study was conducted on the relationship between sales (X, in billions of US dollars) and inventory levels (Y, in billions of US dollars), having a random sample of size 20. You are assigned to build up a simple linear regression model and report the outcomes. Q1. Calculate the descriptive statistics for both Y and X, comprising (however not limited to): n, mean, median, std, min and max. Q2. Illustrate the scatter plot between Y and X. Is a linear model suitable for the data? Q3. Calculate the Pearson and Spearman correlations between Y and X and test the null hypothesis of ? = 0. Q4. Assume that the regression model is Y = ß0 + ß1 X + e, fit the model to the SLR data. Illustrate the regression equation and deduce the meaning of two coefficients.