Mktg 301
7) Data from a small bookstore are shown in the accompanying table. The manager wants to predict Sales from Number of Sales People Working. Number of sales people working | Sales (in $1000) | 4 | 12 | 5 | 13 | 8 | 15 | 10 | 16 | 12 | 20 | 12 | 22 | 14 | 22 | 16 | 25 | 18 | 25 | 20 | 28 | x=11.9 | y=19.8 | SD(x)=5.30 | SD(y)=5.53 |
a) Find the slope estimate, b1. Use technology or the formula below to find the slope. b1=rsysx Enter x,y Data in TI-84 under STAT > STAT > CALC > 8: LinReg(a+bx) b1=1.023 b) What does b1 mean, in this context?
The slope tells how the response variable hanges for a one unit step in the predictor
Thus, an additional; $1,023 of sales associated with each additional sales person working. c) Find the intercept, b0. b0=y-b1x =19.8-1.023(11.9)
For this problem, use technology, rounding to three decimal places. b0=7.622 d) What does b0 mean in this contet? Is it meanful?
The intercept serves as a starting value for the predicitons. It shuld only be interpreted if a 0 value for the predictor variable makes sense for the context of the situation.
On average, $7,622 is expected when 0 sales people are working. It is not meaningful because it does not make sense in this context. e) Write the equation that predicts Sales from Number of Sales People Working.
Recall that the slope of the equation b1=1.023 and the intercept is b0=7.622
Complete the equation.
Sales=7.622+1.023 *(Number of Sales People Working) f) If 19 people are working, what sales do you predict?
Substitute 19 for the number of sales people working in the equation found in the previous step and solve for Sales.
Sales=7.622+1.023 *(Number of Sales People Working) =7.622+1.023*19 Substitute. =27.059 Simplify.
**Note that each unit of Sales represents $1000. Thus, the predicted sales for 19 people working is 27,059 dollars. g) If sales are actually $26,000, what is the value of the residual?
a) Find the slope estimate, b1. Use technology or the formula below to find the slope. b1=rsysx Enter x,y Data in TI-84 under STAT > STAT > CALC > 8: LinReg(a+bx) b1=1.023 b) What does b1 mean, in this context?
The slope tells how the response variable hanges for a one unit step in the predictor
Thus, an additional; $1,023 of sales associated with each additional sales person working. c) Find the intercept, b0. b0=y-b1x =19.8-1.023(11.9)
For this problem, use technology, rounding to three decimal places. b0=7.622 d) What does b0 mean in this contet? Is it meanful?
The intercept serves as a starting value for the predicitons. It shuld only be interpreted if a 0 value for the predictor variable makes sense for the context of the situation.
On average, $7,622 is expected when 0 sales people are working. It is not meaningful because it does not make sense in this context. e) Write the equation that predicts Sales from Number of Sales People Working.
Recall that the slope of the equation b1=1.023 and the intercept is b0=7.622
Complete the equation.
Sales=7.622+1.023 *(Number of Sales People Working) f) If 19 people are working, what sales do you predict?
Substitute 19 for the number of sales people working in the equation found in the previous step and solve for Sales.
Sales=7.622+1.023 *(Number of Sales People Working) =7.622+1.023*19 Substitute. =27.059 Simplify.
**Note that each unit of Sales represents $1000. Thus, the predicted sales for 19 people working is 27,059 dollars. g) If sales are actually $26,000, what is the value of the residual?