App stat questions

Post ID: 3180818

Overview

A multiple regression model has the form

y-estimeted =11+6X+12W

As X increases by 1 unit (holding W constant), Y is expected to

Question 1 options:

	increase by 11 units
	decrease by 11 units
	decrease by 6 units
	increase by 6 units

If the coefficient of determination is a positive value, then the coefficient of correlation

Question 2 options:

	must be zero
	can be either negative or positive
	must be larger than 1
	must also be positive

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and

SSE = 240. The coefficient of determination is

Question 3 options:

0.300

0.192

0.500

0.700

In regression analysis, the variable that is being predicted is the

Question 4 options:

dependent variable

independent variable

is usually x

intervening variable

A measure of goodness of fit for the estimated regression equation is the

Question 5 options:

	sample size
	mean square due to regression
	mean square due to error
	multiple coefficient of determination

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

Question 6 options:

t test

Either a t test or a chi-square test can be used

F test

chi-square test

In order to test for the significance of a regression model involving 5 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

Question 7 options:

	47 and 3
	5 and 41
	3 and 47
	2 and 43

Correlation analysis is used to determine

Question 8 options:

a multiple regression model

a specific value of the dependent variable for a given value of the independent variable

the equation of the regression line

the strength of the relationship between the dependent and the independent variables

The interval estimate of the mean value of y for a given value of x is

Question 9 options:

	confidence interval estimate
	prediction interval estimate
	average regression
	x versus y correlation interval

In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is

Question 10 options:

	0.1785
	0.65
	any positive value
	0.125

Case 1

A study intends to measure the effect of home size and neighborhood rating on sales price. The data are presented below:

Sales Price	Home Size	Rating
180.0	23	5
98.1	11	2
173.1	20	9
136.5	17	3
141.0	15	8
165.9	21	4
193.5	24	7
127.8	13	6
163.5	19	7
172.5	25	2

Sample correlation (Home Size, Rating)	0.043254
Sample correlation (Home Size, Sales Price)	0.937858
Sample correlation (Rating, Sales Price)	0.372738

Based on the Excel Regression Analyses output (you have to make it in Excel) answer the following questions. Use α = .05.

ANOVA: select the correct statement (use α=.05):

Question 11 options:

	Since the significance of the model is 9.57E-08, we reject Ho, and conclude that at least one independent variable is related to Sales Price at alpha is 0.05.
	Since the significance of the model is 9.57E-08, we do not reject Ho, and conclude that at least one independent variable is related to Sales Price.
	Since the significance of the model is 9.57E-08, we reject Ho, and conclude that the two independent variables are related to Sales Price.
	Since the significance of the model is 9.57E-08, we do not reject Ho, and conclude that the independent variables are not related to Sales Price.

Case 1 (continued)

t test. Select the correct conclusion for individual significance testing.

Question 12 options:

	Since the p-value (4.73E-08) is less than α (.05), we do not reject Ho, and conclude that Home Size is not related to Sales Price
	Since the p-value (4.73E-08) is less than α (.05), we reject Ho, and conclude that Home Size is related to Sales Price at 95% confidence
	Since the p-value (4.73E-08) is less than α (.05), we do not reject Ho, and conclude that Home Size is related to Sales Price
	Since the p-value (4.73E-08) is less than α (.05), we reject Ho, and conclude that Home Size is not related to Sales Price

Case 1 (continued)

Coefficients: select the correct statement:

Question 13 options:

	Sales Price increases in one dollar when rating increases in 3.83 points.
	Sales Price increases in 3.83 dollars when rating increases in 1 point.
	Sales Price decreases in one dollar when rating increases in 3.83 points.
	Sales Price decreases in 3.83 dollars when rating increases in 1 point.

Case 1

Multicollinearity: select the correct statement:

Question 14 options:

	Since the absolute value of correlation (Home Size, Sales Price) is greater than .7, there is a problem of multicollinearity.
	Since the absolute value of correlation (Home Size, Rating) is less than .7, there is a problem of multicollinearity.
	Since the absolute value of correlation (Home Size, Sales Price) is greater than .7, there is not a problem of multicollinearity.
	Since the absolute value of correlation (Home Size, Rating) is less than .7, there is not a problem of multicollinearity.

Case 1 continued

Determine the confidence interval CI for variable “Home size”. Make a conclusion about significance of β_1.

Question 15 options:

	At 95 % of confidence β₁is less than 4.86 but more than 2.81. β₁ is not zero, β₁is significant, the variable Home Size and Sales Price are related.
	At 95 % of confidence β₁is less than 40.913 but more than 17.78. β₁ is not zero, the variable Home Size and Sales Price are related.
	At 95 % of confidence β₁is less than 6.15 but more than 5.07.So β₁ is not zero. It means β1is significant and the variable Home Size and Sales Price are related.
	At 95 % of confidence β₁is less than 6.15 but more than 5.07. So β₁ is zero. It means β1is not significant and the variable Home Size and Sales Price are not related.

Case 2

AlwaysGreen is a chain of 27 franchise stores in the nation. A study conducted this year intended to identify the variables that affect Sales. The Excel results presented below estimate Annual Sales (in $ thousands). Assume α =.05.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.996583914
R Square	0.993179497
Adjusted R Square	0.991555568
Standard Error	17.64924165
Observations	27

ANOVA
	df	SS
Regression	5	952538.9415
Residual	21	6541.410344
Total	26	959080.3519

	Coefficients	Standard Error
Intercept	-18.85941416	30.15022791
Number Sq.Ft. (th)	16.20157356	3.544437306
Inventory ($ th)	0.174635154	0.057606068
Amount Spent on Advertising ($ th)	11.52626903	2.5321033
Size of Sales District (th families)	13.5803129	1.770456609
Number of Competing Stores in District	-5.31097141	1.70542654

Conduct the hypotheses for overall significance of the model

Hypotheses are:

Question 16 options:

	Ho: β1=0 Ha: : β1 is not equal to 0 Reject Ho if p-value≤α
	Ho: β1= β2= β3= β4=0 Ha: At least one beta not equal to zero Reject Ho if p-value≤α
	Ho: β1= β2= β3= β4= β5=0 Ha: At least one beta not equal to zero Reject Ho if p-value≤α
	Ho: β1= β2= β3=0 Ha: At least one beta not equal to zero Reject Ho if p-value≤α

Case 2 (continued)

Test statistic F is

Question 17 options:

	12.456
	611.590
	611.0234
	23.48

Case 2 (continued)

Conduct F test (use the solution in the problem 6) and interpret the overall significance of the model. Use α = .05.

Question 18 options:

	p-value is 5.397E-22 Conclusion: Since p-value < α -> Reject Ho. At least one independent variable has a relationship with Annual Sales at 95% confidence.
	p-value is 5.397E-11 Conclusion: Since p-value < α -> Reject Ho. “At least one independent variable has a relationship with Annual Sales”
	p-value is 5.397E-22 Conclusion: Since p-value < α -> Reject Ho. “All independent variables have a relationship with Annual Sales”
	p-value is 5.397E-11 Since p-value < α -> Reject Ho. “All independent variables have a relationship with Annual Sales”

Case 2 (continued)

Conduct t (individual significance) test to determine if ‘Inventory’ has a relationship with ‘Annual Sales’.

t test is

Question 19 options:

	3.341
	1.245
	3.017
	1.236

Case 2 (continued)

Conduct t (individual significance)test to determine if ‘Inventory’ has a linear relationship with ‘Annual Sales’. Use α = .05.

p-value and conclusion must be

Question 20 options:

	p-value is .006 Model is significant
	p-value is .006 conclusion is Since p-value (.006) < α (.05) ->Don't Reject Ho. “Inventory and Annual Salesare not related”
	p-value is .0121 conclusion is Since p-value (.0121) >α (.05) ->Don't Reject Ho. “Inventory and Annual Salesare not related”
	p-value is .006 conclusion is Since p-value (.006) < α (.05) -> At 95 % confidence there is a relationship between Inventory and Annual Sales

Case 1

The following information regarding a

dependent variable Y and an independent

variable X is provided.

EX = 16 E(X-3) (Y -7)

=-8

EX = 28

E(X-I)7=8

n = 4

SST = 42

SSE = 34

Question 1 options:

	Refer to case 1. The slope of the regression function is 0.1
	Refer to case 1. The slope of the regression function is 11
	Refer to case 1. The slope of the regression function is 1
	Refer to case 1. The slope of the regression function is -1

Refer to Case 1. The Y intercept is

Question 2 options:

	0.1
	1
	11
	-1

Refer to Case 1. The coefficient of determination is

Question 3 options:

	-0.1905
	0.1905
	0.4364
	-0.4364

Refer to Case 1. The coefficient of correlation is

Question 4 options:

0.1905

-0.1905

0.4364

-0.4364

Refer to Case 1. The MSE is

Question 5 options:

	17
	8
	34
	42

Refer to Case 1. The point estimate of Y when X = 3 is

Question 6 options:

	11
	14
	8
	0

The following data represent the number of flash drives sold per day at a local computer shop and their prices.

Price (x)	Units Sold (y)
34	3
36	4
32	6
35	5
30	9
38	2
40	1

Refer

to Case 2 data use Excel, Data Analysis, Regression tools and develop a least-squares regression line and explain what the slope of the line indicates.

Question 7 options:

	y-esimated = 29.7857 - 0.7286x The slope indicates that as the price goes up by $1, the number of units sold goes up by 0.7286 units.
	y-estimated = 29.7857 + 0.7286x. The slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units.
	y-esimated = 29.7857 - 0.7286x The slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units.
	None of these alternatives is correct

Refer to Case 2 data use Excel, Data Analysis, Regression tools and find the coefficient of determination and comment on the strength of relationship between x and y.

Question 8 options:

	r ² = .8556; the estimated regression equation explained 85.56% of the variability in y . Good fit.
	r ² = -.8556; the estimated regression equation explained 85.56% of the variability in y . Good fit.
	r²=-0.92; the estimated regression equation explained 92% of the variability in y . Good fit.
	r²=0.76; the estimated regression equation explained 76% of the variability in y . Good fit.

Refer to Case 2 data Perform an F test and determine if the price and the number of flash drives sold are related.

Let alpha = 0.01.

Question 9 options:

F = 29.624 < 36.26; p-value = .0028; reject H_o,

x and y are related

F = 29.624 > 16.26; p-value = .0028<alpha; reject H_o, x and y are related

F = 29.624 > 16.26; p-value = .0028 > alpha; don't reject H_o, x and y are not related

None of these alternatives is correct

Refer to Case 2 perform a t test and determine if the price and the number of flash drives sold are related. Let alpha = 0.01

Question 10 options:

t = -5.4428 p-value = .28; don't reject H_o, x and y are not related

t = 5.4428 p-value = -.0028; reject H_o, x and y are related

t = -5.4428 p-value = .0028; reject H_o, x and y are related

None of these alternatives is correct