Question

Can someone please explain this?

  The international candy association wants to predict chocolate bar prices. They have collected the following data for 16 samples.

Sample	Size	Price	Energy	Protein	Fat	Carbo	Sodium
1	50	0.88	1970	3.1	High	53.2	Low
2	50	0.88	2003	4.6	High	59	Low
3	40	1.15	2057	9.9	Low	60.9	Low
4	80	1.54	1920	5.1	Low	67.5	High
5	45	1.15	2250	7.2	High	59.4	Low
6	78	1.4	2186	7	High	59.7	Low
7	55	1.28	1930	3.5	High	56.4	Low
8	60	0.97	1980	10.2	Low	59.9	High
9	60	0.97	1890	4.7	Low	67.9	High
10	50	1.28	2030	5.6	Low	67.4	High
11	40	1.1	2180	5.5	High	67.3	High
12	55	1.28	1623	2.2	Low	73.3	Low
13	44.5	0.97	1640	3.7	Low	77.9	High
14	75	1.58	2210	8.2	High	57	Low
15	60	1.55	1980	8.5	Low	63.3	Low
16	42.5	1.18	1970	5	Low	69

a. Identify the dependent variable and independent variables.

b. Build a multiple linear regression model to predict chocolate bar price.

c. Can this model be used to make predictions? Explain

Answer 1

First, we change the categorical variables Fat and Sodium to dummy variables.

High=1

Low=0

Sample	Price	Size	Energy	Protein	Fat	Carbo	Sodium
1	0.88	50	1970	3.1	1	53.2	0
2	0.88	50	2003	4.6	1	59	0
3	1.15	40	2057	9.9	0	60.9	0
4	1.54	80	1920	5.1	0	67.5	1
5	1.15	45	2250	7.2	1	59.4	0
6	1.4	78	2186	7	1	59.7	0
7	1.28	55	1930	3.5	1	56.4	0
8	0.97	60	1980	10.2	0	59.9	1
9	0.97	60	1890	4.7	0	67.9	1
10	1.28	50	2030	5.6	0	67.4	1
11	1.1	40	2180	5.5	1	67.3	1
12	1.28	55	1623	2.2	0	73.3	0
13	0.97	44.5	1640	3.7	0	77.9	1
14	1.58	75	2210	8.2	1	57	0
15	1.55	60	1980	8.5	0	63.3	0
16	1.18	42.5	1970	5	0	69	0

Price is the dependent variable and the rest of them are independent variables. Except for sample which is not a variable.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.820176391
R Square	0.672689312
Adjusted R Square	0.454482187
Standard Error	0.172742075
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	6	0.551941581	0.091990263	3.082801772	0.063213291
Residual	9	0.268558419	0.029839824
Total	15	0.8205
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-2.089379783	1.246714852	-1.675908312	0.128074318	-4.909644711	0.730885144
Size	0.012720923	0.00357347	3.559823882	0.006120968	0.004637173	0.020804673
Energy	0.000800291	0.000526591	1.519757621	0.162892016	-0.000390941	0.001991523
Protein	-0.006628177	0.034325074	-0.193100151	0.851167933	-0.084276888	0.071020534
Fat	-0.152258497	0.184657024	-0.824547553	0.430938381	-0.569981706	0.265464711
Carbo	0.018615509	0.011759022	1.583083111	0.147862317	-0.007985246	0.045216264
Sodium	-0.235767157	0.108628126	-2.17040619	0.058075052	-0.481501049	0.009966736

c)

c)

The p-value of F-statistic =0.063 >0.05.

This means that this model is not significant.

We cannot use this model for prediction of the price as its not a good model.

Moreover, p-values of most of the t-statistics of coefficients is greater than 0.05, which also tells us that they are not significant.