Question

Marge N. O’Hara, a senior analyst for a large stock brokerage has been tasked to forecast the weekly closing stock prices for this blue-chip stock for the first four weeks of next year. You are assigned to provide technical support to Ms. O’Hara.

Weekly closing stock prices for all 52 weeks of this year for this blue-chip stock are reported in units of dollars ($).

3.    a.   Perform a simple linear regression of the weekly closing stock prices data on only time. (Hint: Use the week counter as the independent variable.)

Present the output regression report.

b.   State the equation of this trend line.

c.   In terms of goodness-of-fit measures, how good is this model? Why? In particular,

1. State the numerical value of the coefficient of correlation and its interpretation in the specific context of this problem.

2. State the numerical value of the coefficient of determination and its interpretation in the specific context of this problem.

3. State the numerical value of the standard error of the regression and its interpretation in the specific context of this problem.

d.   Perform a hypothesis test to determine the significance of this model. State your decision and conclusion. (Be complete and specific.)

Specifically, is the weekly closing stock price data significantly trended in time? Why? (Be complete and specific.)

e.   State the RMSE of this model.

f.    Using this time series regression, calculate and state the forecasts for the weekly closing stock price expected for the first four weeks of next year (weeks 53, 54, 55, and 56).

week, t	stock price, y
1	267
2	267
3	268
4	264
5	263
6	260
7	256
8	256
9	252
10	245
11	243
12	240
13	238
14	241
15	244
16	254
17	262
18	261
19	265
20	261
21	261
22	257
23	268
24	270
25	266
26	259
27	258
28	259
29	268
30	276
31	285
32	288
33	295
34	297
35	292
36	299
37	294
38	284
39	277
40	279
41	287
42	276
43	273
44	270
45	264
46	261
47	268
48	270
49	276
50	274
51	284
52	304

Answer 1

We enter the data in excel and then goto data > data analysis tab and select regression

Please see the detailed screenshot below

b. State the equation of this trend line.

The regression equation is formed using the coefficients as

y = 251.11 +0.6443*t

c. In terms of goodness-of-fit measures, how good is this model? Why? In particular,

1. State the numerical value of the coefficient of correlation and its interpretation in the specific context of this problem.

The coefficient of correlation is 0.6178 , this means that the variables y and t are moderatley correlated in the positive direction . when one increases the other also increases

2. State the numerical value of the coefficient of determination and its interpretation in the specific context of this problem.

The coefficient of determintation is 0.3816 , this means that the model is able to explain 38.16 % variation in the value of y due to variation in t

3. State the numerical value of the standard error of the regression and its interpretation in the specific context of this problem.

The standard error value is 12.55 , this means the error we would see while making a prediction

d. Perform a hypothesis test to determine the significance of this model. State your decision and conclusion. (Be complete and specific.)

The hypothesis is
H0 : the model is not signficant
H1 : the model is statistically signficant

we check the p value signficant f which is 1.06409E-06
much less than 0.05 , hence we reject the null hypothesis and conclude that the model is statistically signficant

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines