Question

One manufacturer has developed a quantitative index of the​ "sweetness" of orange juice.​ (The higher the​ index, the sweeter the​ juice). Is there a relationship between the sweetness index and a chemical measure such as the amount of​water-soluble pectin​ (parts per​ million) in the orange​ juice? Data collected on these two variables for 24 production runs at a juice manufacturing plant are shown in the accompanying table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness​ (y) from the amount of pectin​ (x).

Run		Sweetness Index		Pectin​ (ppm)
1		5.2		220
2		5.5		229
3		5.9		256
4		5.9		209
5		5.9		223
6		6.1		217
7		5.9		230
8		5.6		270
9		5.7		238
10		5.9		214
11		5.4		408
12		5.6		259
13		5.8		304
14		5.5		258
15		5.3		282
16		5.4		383
17		5.7		269
18		5.4		267
19		5.6		225
20		5.4		260
21		5.9		231
22		5.8		218
23		5.8		248
24		5.9		241

a. Find the least squares line for the data.

Modifying Above y with carety=______+( ______)x

​(Round to four decimal places as​ needed.)

Answer 1

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.466033893
R Square	0.217187589
Adjusted R Square	0.181605207
Standard Error	0.217508029
Observations	24
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.288768999	0.288768999	6.103795611	0.021715315
Residual	22	1.040814335	0.047309742
Total	23	1.329583333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	6.255433229	0.240753284	25.98275346	5.27899E-18	5.756141479	6.754724979
Pectin​ (ppm) (x)	-0.002278032	0.000922061	-2.470586087	0.021715315	-0.00419027	-0.000365794

(A)

The required least square regression line is