Question

A tech company wanted to determine what factors influenced sales in the first week of a new product launch. They identified 3 predictor variables and used a sample size of 8 product launches. Using this data, they performed multiple regression analysis to understand which predictors were significant and how they affected sales. Present the results and insights gained from this analysis.

Answer 1

Using the regression model provided, sales predictions for day 60 and day 90 are calculated based on the given formula. The significance of the correlation coefficient and the interpretation of the least-squares line's slope is explained to better understand their relevance in regression analysis.

Step-by-step explanation:

The multiple regression analysis in question aims to understand determinants of sales growth during new product launches, which falls under the domain of Mathematics, specifically statistics and data analysis.

Given the provided model ý = 101.32 + 2.48x, we can predict sales growth on specific days by substituting the day (x) into the model. For day 60, the predicted sales (ý) would be 101.32 + (2.48 × 60), which calculates to a prediction of $249.12 thousand. Similarly, for day 90, the predicted sales would be 101.32 + (2.48 × 90), equating to $323.92 thousand. These predictions help the company assess potential revenue and make informed decisions about marketing and inventory.

The correlation coefficient is a statistical measure that would tell us the strength and direction of the linear relationship between the independent variables and sales. While the coefficient itself isn't provided here, if computed, a significant correlation coefficient (typically above 0.5 or below -0.5 in absolute terms) would indicate that there is a strong linear relationship, thereby validating the use of a linear model.

Understanding the least-squares line is critical in regression analysis. It is the line that minimizes the sum of the squares of the residuals (the differences between the observed values and the values predicted by the equation). This line gives the best predictions for the dependent variable, given the independent variables. The slope of the least-squares line would indicate how much the dependent variable changes for a one-unit change in the independent variable. If the slope is significant, it suggests that changes in the independent variables have a meaningful influence on the dependent variabl