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## Statistics

### QuestionÂ 1

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The line described by aÂ regression equationÂ attempts to:
Select one:
a.Â pass through as few points as possible.
b.Â pass through as many points as possible.
c.Â minimise the total squared distances from the points.
d.Â minimise the number of points it touches.

### QuestionÂ 2

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A regression analysis isÂ inappropriateÂ when:
Select one:
a.Â You want to make predictions for one variable based on information from another variable.
b.Â You have two numerical variables.
c.Â The pattern of points in the scatterplot forms a reasonably straight line.
d.Â There is a pattern in the plot of residuals versus fitted values.

### QuestionÂ 3

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If theÂ slopeÂ of a regression line is equal to 2.00, this implies:
Select one:
a.Â For every increase of 2.00 on theÂ x-axis theÂ y-axis value is halved.
b.Â For every increase of 2.00 on theÂ x-axis there is an increase of 2.00 on theÂ y-axis.
c.Â For every increase of 1.00 on theÂ x-axis there is an increase of 2.00 on theÂ y-axis.
d.Â Very little.

### QuestionÂ 4

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When testing a linear relation, what are the appropriateÂ null and alternate hypotheses?
Select one:
a.Â H0: Î² = 0,Â Â H1: Î² â‰  0
b.Â H0: Î² â‰ Â 0,Â Â H1: Î² = 0
c.Â H0: bÂ â‰ Â 0,Â Â H1: b = 0
d.Â H0:Â ÂµÂ = 0,Â Â H1: Âµ â‰  0
e.Â H0: b = 0,Â Â H1: b â‰  0
f.Â H0:Â Î±Â = 0,Â Â H1:Â Î±Â â‰  0

### QuestionÂ 5

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Match anyÂ trendsÂ in the scatter plots with the most appropriate descriptions:
 Answer 1Choose…Strong negative relationshipWeak negative relationshipWeak positive relationshipStrong positive relationshipNo relationship Answer 2Choose…Strong negative relationshipWeak negative relationshipWeak positive relationshipStrong positive relationshipNo relationship Answer 3Choose…Strong negative relationshipWeak negative relationshipWeak positive relationshipStrong positive relationshipNo relationship

### QuestionÂ 6

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For the plots above regarding a regression of the percentage of potato chips broken on the percentage of potato content, are all theÂ assumptionsÂ met? Select the best answer.
Select one:
a. No, the relation does not look linear
b. No, the residuals are not evenly spread either side of the horizontal line for the range of x-values
c.Â None of the assumptions appear to be satisfied.
d. No, the histogram of the residuals is not sufficiently symmetric
e. Yes

### QuestionÂ 7

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The regression goodness-of-fit,Â r2, tells us:
Select one:
a.Â The proportion of variability in y accounted for by x.
b.Â All of the above.
c.Â How to determine someone’s score.
d.Â How to describe a relationship.

### QuestionÂ 8

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Which of the following hypotheses could be tested using aÂ chi-square goodness-of-fit test?
Select one:
a.Â Choice of car colour is directly related to measures of extroversion.
b.Â None of the other choices.
c.Â Individuals with red cars are significantly more extroverted than individuals with green, black or silver cars.
d.Â In terms of car colour, more individuals choose a red car, than a green, a black or a silver car.

### QuestionÂ 9

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In a chi-square test of independence, theÂ degrees of freedomÂ for a table with 9 rows and 8 columns will be:
Answer:

### QuestionÂ 10

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Predicting Percentage of Chips Broken:
Regression Analysis: %Broken chips versus %Potato
The regression equation is
%Broken chips =Â 7.93 – 0.151 %Potato
Predictor Â  Â  Coef Â SE Coef Â  Â  T Â  Â  P
Constant Â  Â 7.9301 Â  0.5225 15.18 0.000
%Potato Â  -0.15084 Â 0.05912 _____ 0.012
S = 2.03470 R-Sq = 6.2% R-Sq(adj) = 5.3%

The Minitab output above is from a regression of the percentage of potato chips broken versus the percentage of potato content in those chips. Use the output to answer the following questions.

1. What is the value of a?Â Â (1 dp) Â Â Answer
2. What is the value of b?Â Â (4 dp) Â Â Answer
3. What is the se(b)?Â Â (4dp) Â Â Answer
4. Calculate the absolute value of the test statistic for b.Â Â (2dp) Â Â Answer
5. What is the goodness of fitÂ  (as a percentage)?Â (1 dp) Â Â Answer
6. What is the correlation?Â Â (2 dp)Â Â Â Answer
7. Would youÂ (A)Â reject orÂ (B)Â not reject the hypothesis thatÂ Â Â ?Â Â Â Answer