Question

The cost (in cents) per ounce of a leading liquid laundry detergent in different sizes. (75) Size (ounces) Cost per ounce (C) 16 24.94 32 12.35 54 6.21 100 7.50 a. c. Define the Independent and Dependent variables b. Plot the points on a graph and label the axes Write the regression equation. Use correct notation. d. Perform a hypothesis test to determine if there is significant linear correlation. Be sure to include 2 separate conclusions as shown on the lecture notes. e. Find the expected predicted value given the input value. This is the number written in parenthesis next to the assignment. For example, for #2 find the predicted welfare family size in the year 1980. Answer parts (f) and (g) only if there is significant linear correlation. f. Determine if there are any outliers by graphing. Include the graph with the boundary lines and label the lines. Give the outliers. g. Interpret the slope of the regression line.

Answer 1

a)

Dependent Variable is Cost

Independent Variable is Size

b) Graph

ScatterPlot 30 25 20 Cost 15 . 10 5 0 0 20 40 60 80 100 120 Size

c)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.744
R Square	0.553
Adjusted R Square	0.330
Standard Error	29.870
Observations	4
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2210.53	2210.53	2.48	0.26
Residual	2	1784.47	892.24
Total	3	3995.00
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	91.00	29.75	3.06	0.09	-37.01	219.01	-37.01	219.01
Cost	-3.18	2.02	-1.57	0.26	-11.86	5.51	-11.86	5.51

Size = 91 - 3.18 * Cost

d)

R Square = 0.55 R = 0.74

Linear correlation

$t=\frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}$

r=0.74 , n= 4

t= 1.55

df=n-2 = 4-2=2

P value = 0.26 >0.05

Do not reject Ho

Not significant