Question

1. The data below show the historical relationship between production levels and overhead costs at your company.

a) Construct a scatterplot of y versus x.

b) Find the least-squares regression line (i.e., calculate the coefficients and show the equation) relating overhead costs to production.

c) Graph the regression line on the plot.

It is recommended that you use Excel to create the scatterplot, but do not use the Excel functions to calculate the slope and intercept of the regression line. Make the calculations explicit (either by Excel or by hand) and show how you derive them. You may use Excel to show the calculation process (in tabular form) or you may do the calculations by hand (in equation form).

X	Y
Production	Overhead
5	12
6	11
7	13
8	15
9	16
10	15
11	16

2. Using the data (production, overhead costs) from Question 1 and the Excel “regression” function, show the printout and

a) verify the regression coefficients,

b) determine what percentage of overhead costs is explained by production,

c) find the t-statistic and p-value, and d) find the 90% confidence interval.

3. Continuing with the previous data, use a t test to test the hypothesis H0: ß1 = 0 versus Ha: ß1 ≠ 0 at the 5% level of significance [where ß1 = slope]. State the decision rule, the test statistic, and your decision. What conclusion can be drawn from the result of the test?

4. Continuing with the previous data, use a t test to test the hypothesis H0: ß1 = 1 versus Ha: ß1 ≠ 1 at the 5% level of significance [where ß1 = slope]. State the decision rule, the test statistic, and your decision. What conclusion can be drawn from the result of the test?

Answer 1

Question 1

Part a

Required scatter plot is given as below:

Part b

Required regression model is given as below:

Regression Statistics
Multiple R	0.887244262
R Square	0.787202381
Adjusted R Square	0.744642857
Standard Error	1.010657495
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	18.89285714	18.89285714	18.4965035	0.007709915
Residual	5	5.107142857	1.021428571
Total	6	24
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	7.428571429	1.574995951	4.716565414	0.005258711	3.379915448	11.47722741
Production	0.821428571	0.190996314	4.300756154	0.007709915	0.330456917	1.312400226

Regression equation is given as below:

Y = 7.428571429 + 0.821428571*X

Part c

Required scatter plot is given as below:

Question 2

Part a

Slope = 0.821428571

Y-intercept = 7.428571429

Part b

The coefficient of determination or the value of R square is given as 0.787202381, which means about 78.7% of overhead costs is explained by production.

Part c

t-statistic = 4.300756154

P-value = 0.007709915

(by using excel)

Part d

Confidence interval = β ± t*SE

Confidence interval = 0.821428571 ± 1.943180274*0.190996314

Lower limit = 0.821428571 - 1.943180274*0.190996314

Upper limit = 0.821428571 + 1.943180274*0.190996314

Lower limit = 0.450288302

Upper limit = 1.192568841

Confidence interval = (0.450288302, 1.192568841)