Question

- Using the data given below, calculate the linear correlation between the two variables x and y.

X |
0 |
3 |
3 |
1 |
4 |

y |
1 |
7 |
2 |
5 |
5 |

(a) .794 (b) .878 (c) .497 (d) .543

- Refer to question 4. Assume you are using a 0.05 level of significance; is there a

significant relationship between the two variables x and y?

- Yes (b) no

- The heights (in inches) and pulse rates (in beats per minutes)
for a sample of 40 women were measured and the linear correlation
coefficient was found to be -.458 (based on data from the National
Health Examination Survey). Using a significance level of 0.05, can
you conclude that there is a significant relationship between the
heights and pulse rates of women?
- Yes (b) no

- A scatterplot in which one variable decreases as another
variable increases is an example of a:
- Positive correlation (b) negative correlation

(c) Curvilinear relationship (d) No correlation

- Refer to question 6. How would you describe the relationship
between women’s’ heights and pulse rates?
- Women who are relatively taller tend to have higher pulse rates
- Women who are relatively shorter tend to have lower pulse rates
- Women with higher pulse rates are more likely to be taller than women with lower pulse rates.
- Women with lower pulse rates are more likely to be taller than women with higher pulse rates.

Answer #1

Following table shows the calculations:

X | Y | X^2 | Y^2 | XY | |

0 | 1 | 0 | 1 | 0 | |

3 | 7 | 9 | 49 | 21 | |

3 | 2 | 9 | 4 | 6 | |

1 | 5 | 1 | 25 | 5 | |

4 | 5 | 16 | 25 | 20 | |

Total | 11 | 20 | 35 | 104 | 52 |

Sample size: n = 5

Now,

The coefficient of correlation is :

**Correct option is c.**

Degree of freedom: df=n-2= 5-2 = 3

The critical value of r using critical value table is 0.878

Since r < 0.878 so there is no significant relationship between the variables.

**Answer: no**

A negative correlation between variables X and Y means that
____.
A. the correlation between variables X and Y is very weak
B. scores on variable X has little predicting power on the
corresponding scores on variable Y
C. higher scores on variable X correspond to lower scores on
variable Y and vice versa
D. Higher scores on variable X correspond to higher scores on
variable Y while lower scores on variable X correspond to lower
scores on variable Y...

Suppose the correlation coefficient between two variables is
found to be 0.83. Which of the following statements are true?
small values of one variable are associated with large values of
the other variable
the relationship between the variables is weak
a scatter plot of the points would show an upward trend
low values of one variable tend to be paired with low values of
the other variable
there is a strong positive curvilinear relationship between the
variables
there is a...

Since a sample data shows that a linear correlation coefficient
between two variables is about 0.08, then it rules out a possible
causal relationship between the two variables.
Yes
No

Consider the following data for two variables, x and
y.
x
22
24
26
30
35
40
y
13
22
34
34
41
35
(a) Develop an estimated regression equation for the data of the
form ŷ = b0 +
b1x. (Round
b0 to one decimal place and
b1 to three decimal places.)
ŷ =
(b) Use the results from part (a) to test for a significant
relationship between x and y. Use α =
0.05
Find the value of the...

Determine if the correlation between the two given variables is
likely to be positive or negative, or if they are not likely to
display a linear relationship.
The age of a car and its selling price

Consider the following sample data for two variables. x = 16,
6,4,2 and Y= 5,11,6,8 a. Calculate the sample covariance
Sxy= b. Calculate the sample correlation coefficient
rxy= c. Describe the relationship between x and y. Choose the
correct answer below. A. There is a positive linear relationship
between x and y. B. There is no linear relationship between x and
y. C. There is a perfect negative linear relationship between x and
y. D. There is a perfect positive linear...

The data below shows height (in inches) and pulse rates (in
beats per minute) of a random sample of women. Construct a
scatterplot, find the value of the linear correlation coefficient
r, and find the P-value using α=0.05 Is there sufficient evidence
to conclude that there is a linear correlation between height and
pulse rate?
Full data set
height (x)
65.8
66.8
62.9
62.4
60.5
65.4
62.3
65.3
67.6
62.3
pulse rate (y)
7979
72
89
64
74
70...

Use the data values in the table below to calculate the
correlation between the variables x and y.
x
y
4
30.72
5
30.06
6
26.4
7
23.64
8
19.88
9
19.52
10
14.56
11
13.7
Give your answer to three decimal places.

True or False: Assuming a linear relationship between X and Y,
if the coefficient of correlation (r) equals 0.50, this means that
50% of the variation in the dependent variable (Y) is due to
changes in the independent variable (X).

True or False: Assuming a linear relationship between X
and Y, if the coefficient of correlation (r)
equals 0.50, this means that 50% of the variation in the dependent
variable (Y) is due to changes in the independent variable (X).

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