Statistics

| May 26, 2015

Question 1

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The line described by a regression equation attempts to:

Select one:
a. pass through as few points as possible.
b. pass through as many points as possible.
c. minimise the total squared distances from the points.
d. minimise the number of points it touches.

Question 2

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A regression analysis is inappropriate when:

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

Question 3

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If the slope of a regression line is equal to 2.00, this implies:

Select one:
a. For every increase of 2.00 on the x-axis the y-axis value is halved.
b. For every increase of 2.00 on the x-axis there is an increase of 2.00 on the y-axis.
c. For every increase of 1.00 on the x-axis there is an increase of 2.00 on the y-axis.
d. Very little.

Question 4

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When testing a linear relation, what are the appropriate null and alternate hypotheses?

Select one:
a. H0: β = 0,  H1: β ≠ 0

b. H0: β ≠ 0,  H1: β = 0
c. H0: b ≠ 0,  H1: b = 0
d. H0: µ = 0,  H1: µ ≠ 0
e. H0: b = 0,  H1: b ≠ 0
f. H0: α = 0,  H1: α ≠ 0

Question 5

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Match any trends 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

Question 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 the assumptions 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. None of the assumptions appear to be satisfied.
d. No, the histogram of the residuals is not sufficiently symmetric
e. Yes

Question 7

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The regression goodness-of-fit, r2, tells us:

Select one:
a. The proportion of variability in y accounted for by x.
b. All of the above.
c. How to determine someone’s score.
d. How to describe a relationship.

Question 8

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Which of the following hypotheses could be tested using a chi-square goodness-of-fit test?

Select one:
a. Choice of car colour is directly related to measures of extroversion.
b. None of the other choices.
c. Individuals with red cars are significantly more extroverted than individuals with green, black or silver cars.
d. In terms of car colour, more individuals choose a red car, than a green, a black or a silver car.

Question 9

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

Answer:

Question 10

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Predicting Percentage of Chips Broken:

Regression Analysis: %Broken chips versus %Potato

The regression equation is

%Broken chips = 7.93 – 0.151 %Potato

Predictor     Coef  SE Coef     T     P

Constant    7.9301   0.5225 15.18 0.000

%Potato   -0.15084  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?  (1 dp)   Answer
  2. What is the value of b?  (4 dp)   Answer
  3. What is the se(b)?  (4dp)   Answer
  4. Calculate the absolute value of the test statistic for b.  (2dp)   Answer
  5. What is the goodness of fit  (as a percentage)? (1 dp)   Answer
  6. What is the correlation?  (2 dp)   Answer
  7. Would you (A) reject or (B) not reject the hypothesis that   ?   Answer

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Category: Mathematics

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