Linear Equations and Variables Questionnaire

Description

Question 1 (1 point)

Saved

Which of the following equations are linear?

Question 1 options:

	y+7=3x
	y=6x²+8
	3y=6x+5y²
	y-x=8x²

Question 2 (1 point)

Which of the following equations are linear?

Question 2 options:

	4y=8
	y²=6x³+8
	3y=6x+5y²
	y-x=8x²

Question 3 (1 point)

You decided to join a fantasy Baseball league and you think the best way to pick your players is to look at their Batting Averages.

You want to use data from the previous season to help predict Batting Averages to know which players to pick for the upcoming season. You want to use Runs Score, Doubles, Triples, Home Runs and Strike Outs to determine if there is a significant linear relationship for Batting Averages.

You collect data to, to help estimate Batting Average, to see which players you should choose. You collect data on 45 players to help make your decision.

x1 = Runs Score/Times at Bat

x2 = Doubles/Times at Bat

x3 = Triples/Times at Bat

x4 = Home Runs/Times at Bat

x5= Strike Outs/Times at Bat

Is there a significant linear relationship between these 5 variables and the Batting Average?

If so, what is/are the significant predictor(s) for determining the Batting Average?

See Attached Excel for Data.

Baseball data.xlsx

Question 3 options:

	No, Triples/Times at Bat, p-value = 0.291004037 > .05, No, Triples, are not a significant predictor for Batting Average. Home Runs/Times at Bat, p-value = 0.114060301 > .05, No, Home Runs are not a significant predictor for Batting Average.
	Yes, Triples/Times at Bat, p-value = 0.291004037 > .05, No, Triples, are not a significant predictor for Batting Average. Home Runs/Times at Bat, p-value = 0.114060301 > .05, No, Home Runs are not a significant predictor for Batting Average.
	No, Runs Score/Times at Bat, p-value = 0.000219186 < .05, Yes, Runs Score is a significant predictor for Batting Average. Doubles/Times at Bat, p-value = 0.00300543 < .05, Yes, Doubles are a significant predictor for Batting Average. Strike Outs/Times at Bat, p-value = 0.00000258892 < .05, Yes, Strikes Outs are a significant predictor for Batting Average.
	Yes, Runs Score/Times at Bat, p-value = 0.000219186 < .05, Yes, Runs Score is a significant predictor for Batting Average. Doubles/Times at Bat, p-value = 0.00300543 < .05, Yes, Doubles are a significant predictor for Batting Average. Strike Outs/Times at Bat, p-value = 0.00000258892 < .05, Yes, Strikes Outs are a significant predictor for Batting Average.

Question 4 (1 point)

You are thinking about opening up a Starbucks in your area but what to know if it is a good investment. How much money do Starbucks actually make in a year? You collect data to, to help estimate Annual Net Sales, in thousands, of dollars to know how much money you will be making.

You collect data on 27 stores to help make your decision.

x1 = Rent in Thousand per month

x2 = Amount spent on Inventory in Thousand per month

x3 = Amount spent on Advertising in Thousand per month

x4 = Sales in Thousand per month

x5= How many Competitors stores are in the Area

Approximately what percentage of the variation in Annual Net Sales is accounted for by these 5 variables in this model?

See Attached Excel for Data.

Starbuck Sales data.xlsx

Question 4 options:

	27.62% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model.
	98.24% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model.
	99.11% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model.
	99.25% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model.

Question 5 (1 point)

With Obesity on the rise, a Doctor wants to see if there is a linear relationship between the Age and Weight and estimating a person’s Systolic Blood Pressure. Is there a significant linear relationship between Age and Weight and a person’s Systolic Blood Pressure?

If so, what is/are the significant predictor(s) for Systolic Blood Pressure?

See Attached Excel for Data.

BP data

Question 5 options:

	No, Age, p-value = 0.9388 > .05, No, Age is not a significant predictor for Systolic BP Weight, p-value = 0 .3092 > .05, No, Weight is not a significant predictor for Systolic BP
	No, Age, p-value = 0.001303023 < .05, No, Age is not a significant predictor for Systolic BP Weight, p-value = 0.023799395 < .05, No, Weight is not a significant predictor for Systolic BP
	Yes, Age, p-value = 0.9388 > .05, Yes, Age is a significant predictor for Systolic BP Weight, p-value = 0 .3092 > .05, Yes Weight is a significant predictor for Systolic BP
	Yes, Age, p-value = 0.001303023 < .05, Yes, Age is a significant predictor for Systolic BP Weight, p-value = 0.023799395 < .05, Yes Weight is a significant predictor for Systolic BP

Question 6 (1 point)

You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring.

You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.

x1 = Adult Deer Count

x2 = Annual Rain in Inches

x3 = Winter Severity

Where Winter Severity Index:
- 1 = Warm
- 2 = Mild
- 3 = Cold
- 4 = Freeze
- 5 = Severe

Estimate Fawn Count when Adult Deer Count = 10, Annual Rain = 13.5 and Winter Severity = 4

See Attached Excel for Data.

Deer data.xlsx

Question 6 options:

	5
	3.85
	3.06
	2.95

Question 7 (1 point)

In the context of regression analysis, what is the definition of an influential point?

Question 7 options:

	Observed data points that are far from the least squares line
	Observed data points that are far from the other observed data points in the horizontal direction
	Observed data points that are close to the least squares line
	Observed data points that are close to the other observed data points in the horizontal direction

Question 8 (1 point)

The least squares regression line for a data set is y=2.3?0.1x and the standard deviation of the residuals is 0.13.

Does a case with the values x = 4.1, y = 2.34 qualify as an outlier?

Question 8 options:

Yes

Cannot be determined with the given information

Question 9 (1 point)

The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling.

Weight (lbs.)	Rolling Distance (m.)
59	26
84	43
97	48
56	20
103	59
87	44
88	48
92	46
53	28
66	32
71	39
100	49

Can it be concluded at a 0.05 level of significance that there is a linear correlation between the two variables?

Question 9 options:

yes

Cannot be determined

Question 10 (1 point)

A negative linear relationship implies that larger values of one variable will result in smaller values in the second variable.

Question 10 options:

	True
	False

Question 11 (1 point)

You determine there is a strong linear relationship between two variables using a test for linear regression. Can you immediately claim that one variable is causing the second variable to act in a certain way?

Question 11 options:

	No, the correlation would need to be a perfect linear relationship to be sure.
	No, you should examine the situation to identify lurking variables that may be influencing both variables.
	No, you must first decide if the relationship is positive or negative.
	Yes, a strong linear relationship implies causation between the two variables.

Question 12 (1 point)

Which of the following describes how the scatter plot appears? Select all that apply.

Scatter Plot

Question 12 options:

positive

negative

neither positive or negative

Question 13 (1 point)

The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling.

Weight (lbs.)	Rolling Distance (m.)
59	26
84	43
97	48
56	20
103	59
87	44
88	48
92	46
53	28
66	32
71	39
100	49

Regression Statistics
Multiple R	0.956806
R Square	0.915477
Adjusted R Square	0.907025
Standard Error	3.483483
Observations	12

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1314.32	1314.32	108.3113	1.1E-06
Residual	10	121.3466	12.13466
Total	11	1435.667

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-8.56472	4.7892	-1.78834	0.104007	-19.2357	2.106284
Weight (lbs.)	0.611691	0.058775	10.40727	1.1E-06	0.480731	0.742651

Find the standard error of estimate. Round answer to 4 decimal places.

___

Question 13 options:

Question 14 (1 point)

Body frame size is determined by a person’s wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals.

scatter plot

Model Summary^b
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.734^a	.539	.525	4.01409
a. Predictors: (Constant), Wrist Circumference
b. Dependent Variable: Height

ANOVA^a
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	621.793	1	621.793	38.590	.000^b
	Residual	531.726	33	16.113
	Total	1153.519	34
a. Dependent Variable: Height
b. Predictors: (Constant), Wrist Circumference

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta
1	(Constant)	38.177	5.089		7.502	.000
1	Wrist Circumference	4.436	.714	.734	6.212	.000

What is the value of the test statistic to see if the correlation is statistically significant?

Question 14 options:

	0.539
	7.502
	4.436
	5.089
	6.212
	0.734

Question 15 (1 point)

What are the hypotheses for testing to see if a correlation is statistically significant?

Question 15 options:

	H₀: ? = 0; H₁:?=1
	H₀: ? = ±1 ; H₁:?? ±1
	H₀: r = 0; H₁: r? 0
	H₀: ? = 0; H₁:?? 0
	H₀: r = ±1; H₁: r? ± 1

Question 16 (1 point)

A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed. Calculate the correlation coefficient using technology (you can copy and paste the data into Excel). Round answer to 4 decimal places.

Make sure you put the 0 in front of the decimal.

HW3	Midterm
13.1	59.811
21.9	87.539
8.8	53.728
24.3	95.283
5.4	39.174
13.2	66.092
20.9	89.729
18.5	78.985
20	86.2
15.4	73.274
25	93.25
9.7	52.257
6.4	43.984
20.2	79.762
21.8	84.258
23.1	92.911
22	87.82
11.4	54.034
14.9	71.869
18.4	76.704
15.1	70.431
15	65.15
16.8	77.208

Answer:___

___

Question 16 options:

Question 17 (1 point)

Choose the correlation coefficient that is represented in the scatterplot.

scatter plot

Question 17 options:

0.83

0.15

-0.82

Question 18 (1 point)

The correlation coefficient, r, is a number between:

Question 18 options:

	0 and ?
	-10 and 10
	-? and ?
	0 and 10
	0 and 1
	– 1 and 1

Question 19 (1 point)

HW3	Midterm
13.1	59.811
21.9	87.539
8.8	53.728
24.3	95.283
5.4	39.174
13.2	66.092
20.9	89.729
18.5	78.985
20	86.2
15.4	73.274
25	93.25
9.7	52.257
6.4	43.984
20.2	79.762
21.8	84.258
23.1	92.911
22	87.82
11.4	54.034
14.9	71.869
18.4	76.704
15.1	70.431
15	65.15
16.8	77.208

Find the y-intercept and slope for the regression equation using technology (you can copy and paste the data into Excel). Round answer to 3 decimal places.

?=___+___x

Question 19 options:

Blank # 1

Blank # 2

Question 20 (1 point)

Bone mineral density and cola consumption has been recorded for a sample of patients. Let x represent the number of colas consumed per week and y the bone mineral density in grams per cubic centimeter. Assume the data is normally distributed. A regression equation for the following data is ?=0.8893-0.0031x. Which is the best interpretation of the slope coefficient?

x	y
1	0.883
2	0.8734
3	0.8898
4	0.8852
5	0.8816
6	0.863
7	0.8634
8	0.8648
9	0.8552
10	0.8546
11	0.862

Question 20 options:

	For every additional average weekly soda consumption, a person’s bone density increases by 0.0031 grams per cubic centimeter.
	For every additional average weekly soda consumption, a person’s bone density decreases by 0.0031 grams per cubic centimeter.
	For an increase of 0.8893 in the average weekly soda consumption, a person’s bone density decreases by 0.0031 grams per cubic centimeter.
	For every additional average weekly soda consumption, a person’s bone density decreases by 0.8893 grams per cubic centimeter.