NMIMS Assignment Solution of Decision Science for the April 2024 Examination

Q2. Write the interpretation for the following regression model. You are advised to run the analysis using MS EXCEL.

Here Hiranmayee Dhar, an entrepreneur who is running “Pashminaa” a store of Pashmina shawls. She is targeting customers via social media applications; she has chosen Instagram as a platform and had also chosen REELs to advertise her products. She is looking for a forecasting model to understand the impact of no of likes of the REELs demonstrating product and its sales (in number of units).  (10 Marks)

Reel   Number	Number   of  units sold	Number   of likes
Reel 1	24	1503
Reel 2	24	1564
Reel 3	24	1649
Reel 4	24	1882
Reel 5	26	1924
Reel 6	28	1937
Reel 7	28	1944
Reel 8	29	2086
Reel 9	30	2150
Reel 10	31	2215
Reel 11	32	2366
Reel 12	32	2472
Reel 13	35	2622
Reel 14	35	2792
Reel 15	36	2871
Reel 16	36	2973
Reel 17	38	3000
Reel 18	38	3024
Reel 19	39	3319
Reel 20	40	3336
Reel 21	41	3337
Reel 22	41	3413
Reel 23	41	3479
Reel 24	42	3577
Reel 25	46	3617
Reel 26	46	3922
Reel 27	46	4332
Reel 28	48	4562
Reel 29	48	4577
Reel 30	48	4763
Reel 31	49	4964

Solution Hints:

A regression model is a statistical method used in machine learning and statistics to explore the relationship between a dependent variable and one or more independent variables. The goal of a regression analysis is to understand and quantify the way in which the independent variables influence the dependent variable.

In simpler terms, regression models help in predicting a continuous outcome or response variable based on input features. The relationship between the variables is typically expressed through a mathematical equation, and the model aims to find the best-fit line or curve that minimizes the difference between the predicted values and the actual values of the dependent variable.

There are various types of regression models, including:

1. Linear Regression: Assumes a linear relationship between the independent and dependent variables.
2. Multiple Regression: Extends linear regression to include multiple independent variables.
3. Polynomial Regression: Allows for more complex relationships by using polynomial functions.
4. Ridge Regression and Lasso Regression: Techniques that add regularization terms to the linear regression model to prevent overfitting.
5. Logistic Regression: Despite its name, logistic regression is used for binary classification problems, predicting the probability of an event occurring.

Regression models are widely used in various fields, such as economics, finance, biology, and machine learning, to analyze and predict the behavior of systems based on input variables.

Steps to find out regression model in Excel:

Creating a regression model in Excel involves using the built-in regression analysis tool. Here are the steps to perform linear regression in Excel:

1. Organize Your Data:
   • Ensure that your data is organized with the independent variable (X) in one column and the dependent variable (Y) in another.
2. Open Excel and Load Your Data:
   • Open Excel and load your dataset into a new or existing worksheet.
3. Insert Scatter Plot:
   • Select the data range for both the independent and dependent variables.
   • Go to the “Insert” tab, click on “Scatter” in the Charts group, and choose a scatter plot.
4. Add Trendline:
   • Right-click on a data point on the scatter plot and choose “Add Trendline.”
   • In the “Format Trendline” pane, select the “Linear” option.
5. Display Equation and R-squared:
   • Check the option to “Display Equation on chart” and “Display R-squared value on chart” in the “Format Trendline” pane.
6. Interpret the Results:
   • The equation displayed on the chart represents the formula of the regression line.
   • The R-squared value indicates the goodness of fit, ranging from 0 to 1. A higher R-squared value suggests a better fit.

If you need more advanced regression analysis or want to perform multiple regression, you can use Excel’s Data Analysis ToolPak. Here are the steps:

1. Enable Data Analysis ToolPak:
   • Go to the “File” tab, click on “Options,” and select “Add-ins.”
   • In the “Manage” box, choose “Excel Add-ins” and click “Go.”
   • Check “Analysis ToolPak” and click “OK.”
2. Open Data Analysis ToolPak:
   • Go to the “Data” tab, and you should see “Data Analysis” in the Analysis group.
3. Choose Regression:
   • Select “Regression” from the list of available tools and click “OK.”
4. Input Range and Output Options:
   • Specify the input range for the independent and dependent variables.
   • Choose where you want the regression output to be displayed (either on a new worksheet or a specific range).
5. Interpret the Results:
   • Examine the output table, which includes coefficients, statistical information, and other relevant details about the regression model.

By following these steps, you can perform a regression analysis and obtain valuable insights from your data using Excel.

The concepts of R-square, Multiple R, ANOVA, Significance of Independent variable, and B1 value

R-squared (R²):

• Definition: R-squared is a measure of how well the independent variable(s) explain the variability of the dependent variable in a regression model.
• Interpretation: It is a value between 0 and 1. A higher R-squared indicates a better fit, suggesting that a larger proportion of the variability in the dependent variable is explained by the independent variable(s).

Multiple R:

• Definition: Multiple R is the correlation coefficient between the observed and predicted values in a multiple regression model.
• Interpretation: It represents the strength and direction of the linear relationship between the dependent variable and all the independent variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

ANOVA (Analysis of Variance):

• Definition: In the context of regression, ANOVA assesses the significance of the overall regression model by comparing the variability explained by the model to the unexplained variability.
• Interpretation: The ANOVA table includes the F-statistic and its associated p-value. A low p-value (typically below a significance level like 0.05) suggests that the regression model is statistically significant, meaning that at least one independent variable has a significant effect on the dependent variable.

Significance of Independent Variables:

• Definition: In regression analysis, each independent variable has an associated p-value that indicates its significance in predicting the dependent variable.
• Interpretation: A low p-value (typically below 0.05) for an independent variable suggests that the variable is likely to be a significant predictor of the dependent variable. On the other hand, a high p-value suggests that the variable may not be a significant contributor to the model.

B1 Value (Coefficient for Independent Variable):

• Definition: In a simple linear regression model (with one independent variable), B1 represents the slope of the regression line, indicating the change in the dependent variable for a one-unit change in the independent variable.
• Interpretation: If B1 is positive, it suggests a positive relationship between the variables, meaning that an increase in the independent variable is associated with an increase in the dependent variable. If B1 is negative, it indicates a negative relationship.

Understanding these concepts is crucial for assessing the performance and validity of a regression model, interpreting the relationships between variables, and making informed decisions based on the analysis results.

Note: The regression analysis indicates a robust and highly significant relationship between the number of likes on Instagram REELs and the sales of Pashmina shawls for entrepreneur Hiranmayee Dhar. With a remarkably high R-squared value of 0.9878, nearly 98.78% of the variation in sales can be explained by the number of likes. The coefficient for the number of likes is 0.01176, implying that for each additional like, the number of units sold increases significantly. The low p-value (2.56E-29) reinforces the statistical significance of this relationship. This information is crucial for Hiranmayee, as it provides actionable insights into the effectiveness of her marketing strategy on Instagram. The entrepreneur can leverage this knowledge to optimize social media advertising efforts, emphasizing the impact of garnering likes on REELs for driving Pashmina shawl sales.

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