With milk sales sagging of late, The Milk Processor Education Program (MPEP) decided to move on from the famous "Got Milk" ad slogan in favor of a new one, "Milk Life." The new tagline emphasizes milk's nutritional benefits, including its protein content. MPEP began collecting data on the number of gallons of milk households consumed weekly (in millions), weekly price per gallon, and weekly expenditures on milk advertising (in hundreds of dollars) for the period following the launch of the new campaign. These data are available via the link below. Use these data to estimate a linear regression.

Suppose that the weekly price of milk is $3.40 per gallon and MPEP decides to ramp up weekly advertising by 35 percent to $150 (in hundreds). Use your regression model to estimate the weekly quantity of milk consumed after this advertising increase.

Linear Model Log-Linear Model

Q P A lnQ lnP lnA

4.76 2.46 472.68 1.56 0.90 6.16

0.90 4.28 326.41 -0.10 1.45 5.79

1.74 3.72 357.36 0.55 1.31 5.88

0.96 4.20 475.82 -0.04 1.43 6.17

2.38 4.14 494.25 0.87 1.42 6.20

1.28 4.59 458.62 0.25 1.52 6.13

2.86 3.30 421.67 1.05 1.19 6.04

1.87 4.34 534.85 0.63 1.47 6.28

2.19 3.31 524.75 0.78 1.20 6.26

1.38 3.35 370.35 0.32 1.21 5.91

0.21 4.53 420.16 -1.54 1.51 6.04

3.55 2.63 333.79 1.27 0.97 5.81

2.44 4.40 437.32 0.89 1.48 6.08

1.94 4.36 442.70 0.66 1.47 6.09

2.50 3.24 375.67 0.91 1.18 5.93

2.92 3.45 546.36 1.07 1.24 6.30

4.94 2.97 391.17 1.60 1.09 5.97

2.14 3.22 498.00 0.76 1.17 6.21

3.89 3.34 530.17 1.36 1.20 6.27

6.91 2.24 527.36 1.93 0.81 6.27

3.41 4.04 440.93 1.23 1.40 6.09

1.16 4.10 480.35 0.15 1.41 6.17

1.60 3.99 404.91 0.47 1.38 6.00

4.09 3.22 512.00 1.41 1.17 6.24

2.69 2.98 346.29 0.99 1.09 5.85

2.41 4.30 383.47 0.88 1.46 5.95

2.25 2.84 434.26 0.81 1.04 6.07

2.48 3.96 548.37 0.91 1.38 6.31

3.79 2.49 357.71 1.33 0.91 5.88

3.33 3.29 445.73 1.20 1.19 6.10

2.61 4.02 524.55 0.96 1.39 6.26

2.40 4.05 487.87 0.88 1.40 6.19

3.92 2.46 343.13 1.37 0.90 5.84

3.42 3.45 353.81 1.23 1.24 5.87

0.80 3.40 334.47 -0.23 1.22 5.81

5.79 2.95 330.57 1.76 1.08 5.80

3.58 2.69 363.91 1.28 0.99 5.90

1.58 3.79 383.71 0.46 1.33 5.95

1.14 3.37 430.37 0.13 1.21 6.06

1.04 4.64 501.84 0.04 1.54 6.22

4.88 2.66 447.12 1.59 0.98 6.10

4.31 2.25 404.38 1.46 0.81 6.00

2.23 3.94 449.29 0.80 1.37 6.11

1.38 4.42 327.99 0.32 1.49 5.79

1.62 3.13 332.39 0.49 1.14 5.81

1.38 4.45 450.16 0.33 1.49 6.11

6.20 2.38 467.40 1.82 0.87 6.15

4.17 3.69 528.60 1.43 1.31 6.27

4.08 4.02 533.73 1.41 1.39 6.28

0.08 4.30 355.81 -2.55 1.46 5.87

3.82 2.80 462.42 1.34 1.03 6.14

1.17 4.51 549.78 0.16 1.51 6.31

3.26 2.42 366.63 1.18 0.88 5.90

2.44 4.37 429.74 0.89 1.47 6.06

4.16 2.53 399.57 1.42 0.93 5.99

2.63 3.63 521.95 0.97 1.29 6.26

4.94 2.80 356.59 1.60 1.03 5.88

1.84 4.36 416.24 0.61 1.47 6.03

4.71 3.12 435.99 1.55 1.14 6.08

6.46 2.40 464.62 1.87 0.87 6.14

2.79 3.51 353.37 1.03 1.25 5.87

4.09 3.07 425.12 1.41 1.12 6.05

4.76 2.32 481.72 1.56 0.84 6.18

3.05 3.45 376.30 1.12 1.24 5.93

0.87 4.44 536.86 -0.13 1.49 6.29

3.12 2.50 493.52 1.14 0.92 6.20

1.34 3.11 454.69 0.29 1.13 6.12

1.93 3.24 487.07 0.66 1.17 6.19

1.64 2.87 461.69 0.50 1.05 6.13

4.39 2.97 410.84 1.48 1.09 6.02

5.76 2.33 480.66 1.75 0.84 6.18

4.40 2.82 381.62 1.48 1.04 5.94

6.22 3.14 456.97 1.83 1.14 6.12

1.10 3.89 461.39 0.09 1.36 6.13

4.12 2.67 430.43 1.42 0.98 6.06

5.40 2.73 438.53 1.69 1.01 6.08

2.75 4.52 336.00 1.01 1.51 5.82

5.12 2.28 519.90 1.63 0.83 6.25

3.94 3.25 536.25 1.37 1.18 6.28

5.69 2.18 439.75 1.74 0.78 6.09

0.44 4.27 352.57 -0.82 1.45 5.87

1.89 3.62 397.69 0.64 1.29 5.99

4.02 3.32 345.17 1.39 1.20 5.84

3.70 3.43 507.56 1.31 1.23 6.23

3.26 2.43 330.67 1.18 0.89 5.80

2.98 2.97 433.20 1.09 1.09 6.07

2.09 4.32 462.14 0.74 1.46 6.14

5.68 2.25 515.33 1.74 0.81 6.24

4.33 2.65 508.14 1.47 0.98 6.23

4.97 3.63 510.41 1.60 1.29 6.24

2.89 3.60 343.16 1.06 1.28 5.84

2.25 3.37 365.82 0.81 1.22 5.90

0.17 3.77 425.56 -1.79 1.33 6.05

3.96 2.87 347.36 1.38 1.06 5.85

4.08 2.97 326.06 1.40 1.09 5.79

3.49 3.94 527.12 1.25 1.37 6.27

4.21 4.10 475.28 1.44 1.41 6.16

2.25 4.09 475.69 0.81 1.41 6.16

2.40 3.93 536.42 0.88 1.37 6.28

1.61 4.10 325.89 0.48 1.41 5.79

Question

With milk sales sagging of late, The Milk Processor Education Program (MPEP) decided to move on from the famous "Got Milk" ad slogan in favor of a new one, "Milk Life." The new tagline emphasizes milk's nutritional benefits, including its protein content. MPEP began collecting data on the number of gallons of milk households consumed weekly (in millions), weekly price per gallon, and weekly expenditures on milk advertising (in hundreds of dollars) for the period following the launch of the new campaign. These data are available via the link below. Use these data to estimate a linear regression.

Suppose that the weekly price of milk is $3.40 per gallon and MPEP decides to ramp up weekly advertising by 35 percent to $150 (in hundreds). Use your regression model to estimate the weekly quantity of milk consumed after this advertising increase.

Linear Model			Log-Linear Model
Q	P	A	lnQ	lnP	lnA
4.76	2.46	472.68	1.56	0.90	6.16
0.90	4.28	326.41	-0.10	1.45	5.79
1.74	3.72	357.36	0.55	1.31	5.88
0.96	4.20	475.82	-0.04	1.43	6.17
2.38	4.14	494.25	0.87	1.42	6.20
1.28	4.59	458.62	0.25	1.52	6.13
2.86	3.30	421.67	1.05	1.19	6.04
1.87	4.34	534.85	0.63	1.47	6.28
2.19	3.31	524.75	0.78	1.20	6.26
1.38	3.35	370.35	0.32	1.21	5.91
0.21	4.53	420.16	-1.54	1.51	6.04
3.55	2.63	333.79	1.27	0.97	5.81
2.44	4.40	437.32	0.89	1.48	6.08
1.94	4.36	442.70	0.66	1.47	6.09
2.50	3.24	375.67	0.91	1.18	5.93
2.92	3.45	546.36	1.07	1.24	6.30
4.94	2.97	391.17	1.60	1.09	5.97
2.14	3.22	498.00	0.76	1.17	6.21
3.89	3.34	530.17	1.36	1.20	6.27
6.91	2.24	527.36	1.93	0.81	6.27
3.41	4.04	440.93	1.23	1.40	6.09
1.16	4.10	480.35	0.15	1.41	6.17
1.60	3.99	404.91	0.47	1.38	6.00
4.09	3.22	512.00	1.41	1.17	6.24
2.69	2.98	346.29	0.99	1.09	5.85
2.41	4.30	383.47	0.88	1.46	5.95
2.25	2.84	434.26	0.81	1.04	6.07
2.48	3.96	548.37	0.91	1.38	6.31
3.79	2.49	357.71	1.33	0.91	5.88
3.33	3.29	445.73	1.20	1.19	6.10
2.61	4.02	524.55	0.96	1.39	6.26
2.40	4.05	487.87	0.88	1.40	6.19
3.92	2.46	343.13	1.37	0.90	5.84
3.42	3.45	353.81	1.23	1.24	5.87
0.80	3.40	334.47	-0.23	1.22	5.81
5.79	2.95	330.57	1.76	1.08	5.80
3.58	2.69	363.91	1.28	0.99	5.90
1.58	3.79	383.71	0.46	1.33	5.95
1.14	3.37	430.37	0.13	1.21	6.06
1.04	4.64	501.84	0.04	1.54	6.22
4.88	2.66	447.12	1.59	0.98	6.10
4.31	2.25	404.38	1.46	0.81	6.00
2.23	3.94	449.29	0.80	1.37	6.11
1.38	4.42	327.99	0.32	1.49	5.79
1.62	3.13	332.39	0.49	1.14	5.81
1.38	4.45	450.16	0.33	1.49	6.11
6.20	2.38	467.40	1.82	0.87	6.15
4.17	3.69	528.60	1.43	1.31	6.27
4.08	4.02	533.73	1.41	1.39	6.28
0.08	4.30	355.81	-2.55	1.46	5.87
3.82	2.80	462.42	1.34	1.03	6.14
1.17	4.51	549.78	0.16	1.51	6.31
3.26	2.42	366.63	1.18	0.88	5.90
2.44	4.37	429.74	0.89	1.47	6.06
4.16	2.53	399.57	1.42	0.93	5.99
2.63	3.63	521.95	0.97	1.29	6.26
4.94	2.80	356.59	1.60	1.03	5.88
1.84	4.36	416.24	0.61	1.47	6.03
4.71	3.12	435.99	1.55	1.14	6.08
6.46	2.40	464.62	1.87	0.87	6.14
2.79	3.51	353.37	1.03	1.25	5.87
4.09	3.07	425.12	1.41	1.12	6.05
4.76	2.32	481.72	1.56	0.84	6.18
3.05	3.45	376.30	1.12	1.24	5.93
0.87	4.44	536.86	-0.13	1.49	6.29
3.12	2.50	493.52	1.14	0.92	6.20
1.34	3.11	454.69	0.29	1.13	6.12
1.93	3.24	487.07	0.66	1.17	6.19
1.64	2.87	461.69	0.50	1.05	6.13
4.39	2.97	410.84	1.48	1.09	6.02
5.76	2.33	480.66	1.75	0.84	6.18
4.40	2.82	381.62	1.48	1.04	5.94
6.22	3.14	456.97	1.83	1.14	6.12
1.10	3.89	461.39	0.09	1.36	6.13
4.12	2.67	430.43	1.42	0.98	6.06
5.40	2.73	438.53	1.69	1.01	6.08
2.75	4.52	336.00	1.01	1.51	5.82
5.12	2.28	519.90	1.63	0.83	6.25
3.94	3.25	536.25	1.37	1.18	6.28
5.69	2.18	439.75	1.74	0.78	6.09
0.44	4.27	352.57	-0.82	1.45	5.87
1.89	3.62	397.69	0.64	1.29	5.99
4.02	3.32	345.17	1.39	1.20	5.84
3.70	3.43	507.56	1.31	1.23	6.23
3.26	2.43	330.67	1.18	0.89	5.80
2.98	2.97	433.20	1.09	1.09	6.07
2.09	4.32	462.14	0.74	1.46	6.14
5.68	2.25	515.33	1.74	0.81	6.24
4.33	2.65	508.14	1.47	0.98	6.23
4.97	3.63	510.41	1.60	1.29	6.24
2.89	3.60	343.16	1.06	1.28	5.84
2.25	3.37	365.82	0.81	1.22	5.90
0.17	3.77	425.56	-1.79	1.33	6.05
3.96	2.87	347.36	1.38	1.06	5.85
4.08	2.97	326.06	1.40	1.09	5.79
3.49	3.94	527.12	1.25	1.37	6.27
4.21	4.10	475.28	1.44	1.41	6.16
2.25	4.09	475.69	0.81	1.41	6.16
2.40	3.93	536.42	0.88	1.37	6.28
1.61	4.10	325.89	0.48	1.41	5.79

Accepted Answer

In this question  given that  data on the number of gallons of milk households consumed weekly (in…