Question

McDonald's Nutrition Data

We have information on nutritional content of sandwiches and similar items at McDonald’s: Calories, grams of carbohydrates, milligrams of salt, and meat or non-meat item.

a. Create a dummy variable, Meat, for meat items.

b. Run a regression of Calories on Carbs, Salt and Meat. Write down the estimated regression.

c. Carry out a t-test for the coefficient on Meat. Interpret the results in the context of the problem.

d. Interpret the coefficient on Meat in the context of the problem.

Calories	Carbs	Salt	Item
110	12	0.5123	Non-Meat
140	33	0	Non-Meat
170	10	6.7742	Meat
230	22	10.2597	Non-Meat
230	56	0	Non-Meat
240	23	6	Non-Meat
290	25	7.6136	Non-Meat
300	35	9.6512	Meat
320	30	4.3089	Meat
320	40	5.0549	Non-Meat
340	52	4.1593	Non-Meat
360	46	5.8974	Non-Meat
370	31	5.5147	Non-Meat
390	46	3.9286	Non-Meat
440	51	6.5741	Non-Meat
440	79	0.8564	Non-Meat
450	37	4.5946	Meat
480	30	3.3721	Meat
500	26	6.6667	Meat
500	95	1.0353	Non-Meat
500	95	0.8235	Non-Meat
510	35	9.084	Meat
550	52	4.3023	Meat
570	32	5.1777	Meat
610	32	5.7073	Meat
650	38	8.4656	Meat
680	53	3.3813	Meat
710	67	4.5627	Meat
780	55	4.5875	Meat
920	53	2.8895	Meat
1020	55	3.8624	Meat

  

Answer 1

1)

Calories	Carbs	Salt	Item	Meat
110	12	0.5123	Non-Meat	0
140	33	0	Non-Meat	0
170	10	6.7742	Meat	1
230	22	10.2597	Non-Meat	0
230	56	0	Non-Meat	0
240	23	6	Non-Meat	0
290	25	7.6136	Non-Meat	0
300	35	9.6512	Meat	1
320	30	4.3089	Meat	1
320	40	5.0549	Non-Meat	0
340	52	4.1593	Non-Meat	0
360	46	5.8974	Non-Meat	0
370	31	5.5147	Non-Meat	0
390	46	3.9286	Non-Meat	0
440	51	6.5741	Non-Meat	0
440	79	0.8564	Non-Meat	0
450	37	4.5946	Meat	1
480	30	3.3721	Meat	1
500	26	6.6667	Meat	1
500	95	1.0353	Non-Meat	0
500	95	0.8235	Non-Meat	0
510	35	9.084	Meat	1
550	52	4.3023	Meat	1
570	32	5.1777	Meat	1
610	32	5.7073	Meat	1
650	38	8.4656	Meat	1
680	53	3.3813	Meat	1
710	67	4.5627	Meat	1
780	55	4.5875	Meat	1
920	53	2.8895	Meat	1
1020	55	3.8624	Meat	1

b)

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2.797382	100.0743	0.027953	0.977905	-202.538	208.1329	-202.538	208.1329
Carbs	6.28991	1.404727	4.477673	0.000124	3.407647	9.172173	3.407647	9.172173
Salt	7.167511	10.79579	0.663917	0.512373	-14.9836	29.31864	-14.9836	29.31864
Meat	282.7091	51.56453	5.482626	8.35E-06	176.9074	388.5107	176.9074	388.5107

y = 2.797382 + 6.28991 x1 + 7.167511 x2 +282.7091 x3

c)

Ho:   ß = 0                  
Ha:   ß ╪ 0                  
                      
n =   31                  
alpha,α =    0.05                  
estimated slope=   282.7090598                  
std error =    51.56453084                  
                      
t-test statistic =    t = estimated slope / std error =   282.7090598   /   51.56453084   =   5.483
                      
Df =    n - 2 =   29              
p-value =    0.0000   [excel function: =t.dist.2t(t-stat,df) ]

d)

decision:   p value < α , so, reject the null hypothesis                  
                      
Hence Meal Coefficient cannot be ignored.

  

Please revert back in case of any doubt.

Please upvote. Thanks in advance.