Question

The following table gives information on the calorie count and grams of fat for the11types of bagels produced by Panera Bread.

Bagel	Calories	Fat (grams)
Asiago Cheese	330	5.0
Blueberry	330	2.2
Chocolate Chip	370	5.8
Cinnamon Crunch	430	8.0
Cinnamon Swirl & Raisin	320	1.5
Everything	300	2.9
French Toast	350	5.6
Jalapeno & Cheddar	310	2.2
Plain	290	2.4
Sesame	310	1.7
Sweet Onion & Poppyseed	390	6.9

a. Find the least squares regression line with calories as the dependent variable and fat content as the independent variable.

Round your answers to three decimal places.

y^=Enter you answer to the field 1 in accordance to the question statement+Enter you answer to the field 2 in accordance to the question statementx

b. Make a95%confidence interval forB.

Round your answers to three decimal places.

Enter your answer; confidence interval, lower bound to Enter your answer; confidence interval, upper bound

c. Test at the5%significance level whetherBis different from14.

Based on a5%significance level test, we conclude thatBChoose the answer from the menu in accordance to the question statementChoose the answer from the menu in accordance to the question statement                                                                      isis not different from14.

Answer 1

Following is the output of regression analysis;

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.898916106
R Square	0.808050166
Adjusted R Square	0.786722406
Standard Error	19.64277363
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	14618.36209	14618.36209	37.8872507	0.000167653
Residual	9	3472.547002	385.8385557
Total	10	18090.90909
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	272.3555647	12.35415611	22.0456632	3.84024E-09	244.408522	300.3026074
Fat (grams), X	16.60834363	2.698235028	6.155262033	0.000167653	10.50451194	22.71217531

(a)

The least squares regression line with calories as the dependent variable and fat content as the independent variable is

y' = 272.356 + 16.608*x

(b)

The 95% confidence interval for slope is

lower bound = 10.505

upper bound = 22.712

(c)

Hypotheses are:

The test statistics is

Degree of freedom: df= n-2= 11 -2 = 9

The p-value using excel function "=TDIST(0.967,9,2)" is 0.3588

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.