Question

# The scatter plot below shows the average cost of a designer jacket in a sample of years between 2000 and 2015. The least squares regression line model

Modeling data distributions
The scatter plot below shows the average cost of a designer jacket in a sample of years between 2000 and 2015. The least squares regression line modeling this data is given by $$\widehat{y}=-4815+3.765x.$$ A scatterplot has a horizontal axis labeled Year from 2005 to 2015 in increments of 5 and a vertical axis labeled Price (\$) from 2660 to 2780 in increments of 20. The following points are plotted: $$(2003, 2736), (2004, 2715), (2007, 2675), (2009, 2719), (2013, 270)$$. All coordinates are approximate. Interpret the y-intercept of the least squares regression line. Is it feasible? Select the correct answer below: The y-intercept is −4815, which is not feasible because a product cannot have a negative cost. The y-intercept is 3.765, which is not feasible because an expensive product such as a designer jacket cannot have such a low cost. The y-intercept is −4815, which is feasible because it is the value from the regression equation. The y-intercept is 3.765 which is feasible because a product must have a positive cost.

2020-12-28

Step 1

Given least square regression line $$\widehat{y}=-4815+3.765x.$$ it is to estimate the average cost of designer jacket in a sample of years between 2000 and 2015. The least square regression line is in the form of $$\widehat{y} = mx + b.$$ Where m is the slope of the line and b is the hat y intercept (value of $$\widehat{y}, \text{where } x = 0).$$

Step 2

From the given regression line, it can be observed that y- intercept is -4.815. Here, -4.815 represents the cost and it shows negative. In this case, the product cannot have a negative cost. Therefore, it is not feasible. Hence, the correc option is "the y- intercept is -4.815, which is not feasible because a product cannot have a negative cost".