Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (Each pair of variables has a significant​ correlation.) Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. The caloric content and the sodium content​ (in milligrams) for 6 beef hot dogs are shown in the table below. font size decreased by 1 font size increased by 1 Calories comma x 160 170 130 120 90 190 ​(a) xequals180 calories ​(b) xequals100 calories ​Sodium, y 415 465 350 370 270 530 ​(c) xequals150 calories ​(d) xequals220 calories Find the regression equation. ModifyingAbove y with caretequals nothingxplus​( nothing​) ​(Round to three decimal places as​ needed.) Choose the correct graph below. A. 0 200 0 560 Calories Sodium (mg) A scatterplot has a horizontal axis labeled "Calories" from 0 to 200 in increments of 20 and a vertical axis labeled "Sodium (in milligrams)" from 0 to 560 in increments of 40. The following points are plotted: 90 units to the right of and 270 units above the origin; 120 units to the right of and 370 units above the origin; 130 units to the right of and 350 units above the origin; 160 units to the right of and 415 units above the origin; 170 units to the right of and 465 units above the origin; 190 units to the right of and 530 units above the origin. A line rises from left to right and passes through the points (50, 173) and (100, 295). All coordinates are approximate. B. 0 200 0 560 Calories Sodium (mg) A scatterplot has a horizontal axis labeled "Calories" from 0 to 200 in increments of 20 and a vertical axis labeled "Sodium (in milligrams)" from 0 to 560 in increments of 40. The following points are plotted: 10 units to the right of and 250 units above the origin; 20 units to the right of and 110 units above the origin; 30 units to the right of and 265 units above the origin; 40 units to the right of and 315 units above the origin; 70 units to the right of and 170 units above the origin; 70 units to the right of and 230 units above the origin. A line falls from left to right and passes through the points (0, 202) and (83, 0). All coordinates are approximate. C. 0 200 0 560 Calories Sodium (mg) A scatterplot has a horizontal axis labeled "Calories" from 0 to 200 in increments of 20 and a vertical axis labeled "Sodium (in milligrams)" from 0 to 560 in increments of 40. The following points are plotted: 100 units to the right of and 285 units above the origin; 100 units to the right of and 320 units above the origin; 130 units to the right of and 420 units above the origin; 140 units to the right of and 400 units above the origin; 180 units to the right of and 480 units above the origin; 100 units to the right of and 320 units above the origin. A line rises from left to right and passes through the points (50, 179) and (100, 301). All coordinates are approximate. D. 0 200 0 560 Calories Sodium (mg) A scatterplot has a horizontal axis labeled "Calories" from 0 to 200 in increments of 20 and a vertical axis labeled "Sodium (in milligrams)" from 0 to 560 in increments of 40. The following points are plotted: 70 units to the right of and 170 units above the origin; 100 units to the right of and 270 units above the origin; 110 units to the right of and 80 units above the origin; 130 units to the right of and 315 units above the origin; 130 units to the right of and 365 units above the origin; 150 units to the right of and 430 units above the origin. A line falls from left to right and passes through the points (0, 402) and (166, 0). All coordinates are approximate. ​(a) Predict the value of y for xequals180. Choose the correct answer below. A. 586.115 B. 488.995 C. 416.155 D. not meaningful ​(b) Predict the value of y for xequals100. Choose the correct answer below. A. 586.115 B. 416.155 C. 294.755 D. not meaningful ​(c) Predict the value of y for xequals150. Choose the correct answer below. A. 294.755 B. 416.155 C. 488.995 D. not meaningful ​(d) Predict the value of y for xequals220. Choose the correct answer below. A. 488.995 B. 586.115 C. 294.755 D. not meaningful

Answer 1

(a)scatter plot is given as and the regression equation is y^=51.95+2.428x

(a) right choice is B. 488.995

x=180 calories ​, y^=51.95+2.428*180=488.99,

(b) right choice is C. 294.755

x=100 calories ​, y^=51.95+2.428*100=294.75

​(c)right choice is B. 416.155

x=150 calories, y^=51.95+2.428*150=416.15

​(d) right choice is B. 586.115

x=220 calories, y^=51.95+2.428*220=586.11

following regression analysis information has been generated using ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.976327
R Square	0.953214
Adjusted R Square	0.941517
Standard Error	22.07169
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	39701.36	39701.36	81.49559	0.000834
Residual	4	1948.639	487.1597
Total	5	41650
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	51.95545	39.59284	1.312243	0.259673	-57.9719	161.8828	-57.9719	161.8828
X Variable 1	2.428218	0.26898	9.027491	0.000834	1.681409	3.175027	1.681409	3.175027