This question illustrates an accounting application of regression analysis. A company that manufactures xyz brand of laundry detergent wishes to estimate its fixed and variable production cost. The firm has collected cost data for the last 52 weeks (REFERENCE TABLE DATA BELOW).

Some background information to solve this problem

When you set up the hypothesis, it would be a 'single tail' hypothesis. In class we saw how to solve a two-tail hypothesis test using confidence intervals. That is, to solve for a two-tail hypothesis test the steps are as follows...

1. Access a (1-) confidence interval
2. If the Null hypothesis has any overlap with the confidence interval, then you do not reject the Null hypothesis

Similarly, to solve for a single-tail hypothesis the steps are as follows...

1. Access a (1-2) confidence interval.
2. If the Null hypothesis has any overlap with the confidence interval, then you do not reject the Null hypothesis
3. For example, if the Null hypothesis is H₀: 100.5 and we wish to do this hypothesis test, we will access a (1-2) or 90% confidence interval. Let us say the interval is [-1.23, -0.055],note that the Null hypothesis does have an overlap with the interval because 100.5 has an overlap with [-1.23,-0.055], so we will not rejectthe Null hypothesis.

(Hint: Remember, you will invest if you can convince yourself that the marginal of production at this company is less than $1.55 per unit, it does not say less than equal to $1.55. Also remember the tip that a Null hypothesis cannot have a "<", ">" or "" signs)

You are to perform the following tasks:

(a)Estimate the regression equation for the total cost as a function of the number of cases produced. Copy and paste the regression output below.

(b)What is your estimate of fixed cost?

(Hint: The 'fixed' cost can be thought of as the cost with NO cases produced. Take a look at the cost (y) as specified by your regression equation when x=0.)

(c) What is the marginal cost of producing an additional unit?

(Hint: The marginal cost is the incremental cost of producing each additional unit; how much higher are costs as you move from x to x+1?)

(d)How well does the equation fit the data

(Hint: what is the R² value and what is its interpretation)?

(e)Estimate the total cost when the weekly production is 150,000 cases (Hint: Using your regression equation, plug "150,000" in for the number of cases, and calculate the predicted cost.)

(f) Test whether the slope coefficient (the coefficient on No. of cases produced) of your regression equation is equal to 0 at the 5% significance level (i.e.a = 5%). Put another way, here you will test whether there is any association between cost and production volume at the 5% significance level (a = 5%). (Please explicitly state your hypotheses, your decision rule, and conclusion).

(g)As an investor you are evaluating investing in this company. However, from your prior experience you are concerned about the marginal cost of production at this company. You will only invest if you can convince yourself that the marginal cost of production at this company is less than $1.55 per unit. You see the regression results and note that the marginal cost of production is $1.48 per unit. This gives you some satisfaction, however you understand that these results are but from a sample of data. You want a more rigorous analysis before you invest. Please set up and test a hypothesis to aid your decision. (Please state your hypotheses, your decision rule, and conclusion).

REFERENCE TABLE DATA BELOW:

Week	No_of_Cases_Produced	Total_Cost_$
1	191813	352094.2
2	144116	280548.3
3	172224	322710.8
4	178648	344825.2
5	149703	288928.8
6	175373	327434.9
7	154949	295448.7
8	125708	254436.7
9	116277	238790.9
10	147259	285263
11	169908	305736.3
12	141693	251914.7
13	169487	307164.3
14	191056	336083.6
15	144509	292210.8
16	159684	312092.1
17	176116	318042.6
18	173198	300548.1
19	135210	246413.6
20	159826	279702.2
21	146992	296275.8
22	132130	252890.5
23	154330	274524.4
24	169702	328407.2
25	191342	339019
26	127862	248082.4
27	122440	254198.8
28	189226	329982.7
29	174855	333890
30	117019	247776.8
31	191577	363973.3
32	142659	264380.6
33	144896	255948
34	160732	307694
35	168586	307870.4
36	147794	287545.2
37	124230	230295.8
38	166431	294668.8
39	135975	267929.8
40	135244	249920.1
41	155834	298862.9
42	135183	241710.2
43	141125	279369
44	178705	333371.2
45	156876	290916.3
46	181266	313735.8
47	120948	234973.2
48	172823	306052.7
49	145382	294423.7
50	117995	234295.6
51	126938	250492.4
52	177835	313726