attempting to analyze the relationship between costs and sales, the owner of a fashion shop recorded the…

attempting to analyze the relationship between costs and sales, the owner of a fashion shop recorded the monthly costs ($ thousands) and the sales ($ millions) for a sample of 15 months. and completed a regression model for sales vs costs (i.e., y = sales, x = costs). the coefficient of determination for this data is $r^{2}=0.4763$ and the regression equation is: $hat{y}=-1.329 - 0.5127x$. for part (a), express your answer in percent form (i.e. 3.00% instead of 0.03) and give at least 2 decimal places. (a) what percent of the variation in sales cannot be explained due to the cost factors? for parts (b) and (c), give at least 4 decimal places. (b) calculate the correlation coefficient $r$. (c) what is the slope of the equation? for part (d), give at least 1 decimal place. (d) what would be the best predicted sales for the costs of $39,000? (note x is in thousands) ($ millions)

attempting to analyze the relationship between costs and sales, the owner of a fashion shop recorded the monthly costs ($ thousands) and the sales ($ millions) for a sample of 15 months. and completed a regression model for sales vs costs (i.e., y = sales, x = costs). the coefficient of determination for this data is $r^{2}=0.4763$ and the regression equation is: $hat{y}=-1.329 - 0.5127x$. for part (a), express your answer in percent form (i.e. 3.00% instead of 0.03) and give at least 2 decimal places. (a) what percent of the variation in sales cannot be explained due to the cost factors? for parts (b) and (c), give at least 4 decimal places. (b) calculate the correlation coefficient $r$. (c) what is the slope of the equation? for part (d), give at least 1 decimal place. (d) what would be the best predicted sales for the costs of $39,000? (note x is in thousands) ($ millions)

Answer

Explanation:

Step1: Identify the regression equation

The regression equation is $\hat{y}=- 1.329 - 0.5127x$, where $x$ is cost (in thousands) and $\hat{y}$ is predicted sales (in millions).

Step2: Substitute the value of $x$

The cost $x = 39$ (since $x$ is in thousands and the cost is $39000$). Substitute $x = 39$ into the regression equation: $\hat{y}=-1.329-0.5127\times39$ $=-1.329 - 20.0953$ $=-21.4243$

Answer:

$-21.4$