Question

A.) Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using the listed​ actress/actor ages in various​years, find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 34 years. Is the result within 5 years of the actual Best Actor​ winner, whose age was 52 years?

Best Actress	29	29	29	58	34	33	46	28	64	23	45	54
Best Actor	44	37	37	43	52	48	58	48	39	57	46	34

find the equation of the regression line.

Graph the regression line on the scatterplot. In this​ case, the regression line does not fit very well because the data do not appear to be linear.

Use the regression equation for predictions only if the linear correlation coefficient r indicates that there is a linear correlation between the two variables. Use technology to calculate the linear correlation​ coefficient, rounding to three decimal places. what is r=

p-value:

x and y overbary.:

B.) Different hotels in a certain area are randomly​ selected, and their ratings and prices were obtained online. Using​ technology, with x representing the ratings and y representing​ price, we find that the regression equation has a slope of 130 and a​ y-intercept of −356. Complete parts​ (a) and​ (b) below.

a. What is the equation of the regression​ line? Select the correct choice below and fill in the answer boxes to complete your choice.

b.  What does the symbol ŷ with caret ​represent? (choose the correct answer from 1-4)

1.The symbol ŷ with caret represents the average price of hotels in the area.

2.The symbol ŷ with caret represents the expected price when the​ hotel's rating is 0.

3.The symbol ŷ with caret represents the predicted value of price.

4.The symbol ŷ with caret represents the amount that price increases with a​ 1-point increase in rating.

c.) Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. (draw scatterplot)

x	7	10	13	4	11	9	12	6	3	5	8
y	7.60	8.56	6.34	3.44	8.18	8.60	7.44	6.56	1.34	5.18	8.28

y^ = __ + ___ x (round to 2 decimal places as needed)

b1=

The intercept formula contains the means of x and y. Find each mean by dividing ∑x and ∑y by​ n, rounding to six decimal places as needed.

-x=

-y=

b0=

Answer 1

A) Solution :

Regression Statistics
Multiple R	0.31271
R Square	0.097787
Adjusted R Square	0.007566
Standard Error	7.776297
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	65.54198	65.54198	1.083862	0.322351
Residual	10	604.708	60.4708
Total	11	670.25
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	52.31297	7.145978	7.320617	2.54E-05	36.39074	68.2352	36.39074	68.2352
X Variable 1	-0.17957	0.17248	-1.04109	0.322351	-0.56388	0.204743	-0.56388	0.204743

the equation of the regression line is

P value = 0.3224

xbar = 472/12 = 39.3333

ybar = 543/12 = 45.25

the best predicted age of the Best Actor winner

yhat = 52.313 - 0.18 * 34

yhat = 46.193

y - yhat = 52 - 46.193 = 5.807

result is beyond 5 years.

B) Solution :

a)

slope is 130

intercept is -356

the equation of the regression​ line is

y = -356 + 130 x

b)

Option 3

C) Solution :

yhat = 2.50 + 0.50 x

b1 = 0.5

xbar = 88/11 = 8

ybar = 71.52/11 = 6.502

b0 = 2.50