Positive Correlation

Positive Correlation

Question 1

a.    Positive Correlation
b.    Negative Correlation
c.    No association

Question 2

Calculate the Pearson Correlation Coefficient for these two variables.
ID    Hours of Study (x)    Exam Score (y)    xy    x2    y2
1    2    80    160         6400
2    3    83    249         6889
3    5    95    475         9025
4    1    79    79         6241
5    2    84    168         7056
6    3    90    270         8100
Answer
A.    .81
B.    .96
C.    .91
D.    .75
E.    .85

Question 3

There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by: height = 50.3 + 6.01(age) where height is measured in cm and age in years. Which of the following is NOT CORRECT?

Answer
a.    The estimated slope is 6.01 which implies that children increase by about 6 cm for each year they grow older.
b.    The estimated intercept is 50.3 cm which implies that children reach this height when they are 50.3/6.01=8.4 years old.
c.    The estimated height of a child who is 10 years old is about 110 cm.
d.    My niece is about 8 years old and is about 115 cm tall. She is taller than average.
e.    The average height of children when they are 5 years old is about 50% of the average height when they are 18 years old.

Question 4

A surgery intern has conducted a study of the sleeping habits of her colleagues and has developed a following regression equation: Y = 6 + 0.1X, where X is the number of hours working on one shift, and Y is the number of hours sleeping at night after that shift. Each work shift analyzed was between 8 and 24 hours long. All the following statements about the regression equation are true EXCEPT

Answer
a.    The maximum amount of sleep an intern would get is 8.4 hours
b.    The minimum amount of sleep an intern would get is 6.8 hours
c.    For each hour working on a shift, interns slept an additional 0.1 hours
d.    The minimum amount of sleep an intern would get is 6 hours

Question 5

The effects of a toxic pollutant upon fish was examined by placing fish in a solution of water with various concentrations of the pollutant. The time (in minutes) until the fish showed distress was recorded at which the fish were removed from the container. A total of 18 different experiments were performed. Note that the pollutant is measured on a logarithmic scale where a change of one unit represents an increase of 10 fold in the pollution concentration. A scatterplot and the fitted regression line are shown below: Which of the following is the best description of this plot?

a. Y = 20 – 6X
b. Y = 20 + 4X
c. Y = 20 + 2X
d. Y = 20 – 2X
e. Y = 20 + 6X

Question 6

A selection of cereals was sampled and the number of calories was plotted against the number of grams of protein with the following results: Which of the following is NOT CORRECT?
a. Cereals with 2 grams of protein are estimated to have 106.68 calories/serving.
b. Cereals with 5 grams of protein are estimated to have 106.99 calories/serving.
c. The observed regression line is Y = 106.0 + .339(protein)
d .It is estimated that cereals with no protein would have 106 calories/serving.
e. Each additional gram of protein increase the estimated calorie content per serving by .339 calories.

Question 7

One concern about the depletion of the ozone layer is that the increase in UV light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV levels – measured in Dobson units (du.). At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: The regression model is:
Answer
a.    Y = 3.98 – .05(UV)
b.    Y = -.05 + 3.98(UV)

Question 8

The linear regression equation is determined as follows: Y = a + ßX + e. Match each description below with the appropriate equation characteristic.
Dependent variable
Independent variable
Intercept
Regression coefficient
Error
a)    Y
b)    a
c)    ß
d)    e
e)    x


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