Question

Data from a sample of 10 pharmacies are used to examine the relationship between prescription sales volume and the percentage of prescription ingredients purchased directly from the supplier. The sample data is given below (Use formula to answer each question).

percent ingredient 10 18 25 40 50 63 42 30 5 55

sales volume in $1000 25 55 50 75 110 138 90 60 10 100

a. Draw scatter plot between percent ingredient (x-variable) and the sale volume (y variable). What can you say about the association between percent ingredient and the sale volume?

b. Calculate the mean and standard deviation for both predictor (% ingredient) and the response (sale volume) and sample correlation coefficient . ?

c. Use the information from part (a) above to determine the regression parameters (slope and intercept) using formula.

d. Interpret the slope in the context.ˆ

e. Write the equation of the regression line to predict sale volume from % ingredient

.f. Briefly describe goodness of fit of the fitted model that you have in part (d) above.g. Use the model to predict the sale volume when percent ingredient is 35%. Interpret the predicted value.

Answer 1

a)

Scatter plot is given below:

In the above scatter plot we see that the data show an uphill pattern as move from left to right, this indicates a positive relationship between Percent ingredient (X) and Sales volumes (Y). As the Percent ingredient (X) increase (move right), the Sales volumes (Y) tend to increase (move up).

b)

	percent ingredient (x)	sales volume(y)	xy	x2	y2
	10	25	250	100	625
	18	55	990	324	3025
	25	50	1250	625	2500
	40	75	3000	1600	5625
	50	110	5500	2500	12100
	63	138	8694	3969	19044
	42	90	3780	1764	8100
	30	60	1800	900	3600
	5	10	50	25	100
	55	100	5500	3025	10000
sum	338	713	30814	14832	64719

Here

n = 10

The mean for predictor (% ingredient) is 33.8

The mean for response (sale volume) is 71.3

  

The standard deviation for predictor (% ingredient) is 19.4582

  

The standard deviation for response (sale volume) is 39.2741

The formula for correlation coefficient is

The sample correlation coefficient,r = 0.9763

c)

The formula for finding slope is

The slope is 1.9705

The formula for finding intercept is

The intercept is 4.697

d)

The slope is 1.9705. The slope means that for every one unit increase of percent ingredient we expect that on average sales volume will increase by 1.9705.

e)

Here

The equation of the regression line

g)

Given percent ingredient (x) = 35%

The equation of the regression line

So,

The predicted sale volume when percent ingredient is 35% = 73.66