Question

Use the following information for problems 17-19:

Given the following data:

x |
1 | 2 | 3 | 4 | 5 | 6 |

y |
22 | 31 | 28 | 41 | 33 | 41 |

Which of the following would be the LSRL for the given data?

Determine the correlation coefficient for the data?

Find the residual value for *x* = 5.

Answer #1

Solution :

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

1 | 22 | 22 | 1 | 484 |

2 | 31 | 62 | 4 | 961 |

3 | 28 | 84 | 9 | 784 |

4 | 41 | 164 | 16 | 1681 |

5 | 33 | 165 | 25 | 1089 |

6 | 41 | 246 | 36 | 1681 |

n | 6 |

sum(XY) | 743.00 |

sum(X) | 21.00 |

sum(Y) | 196.00 |

sum(X^2) | 91.00 |

sum(Y^2) | 6680.00 |

Numerator | 342.00 |

Denominator | 418.00 |

r | 0.8182 |

r square | 0.6694 |

Xbar(mean) | 3.5000 |

Ybar(mean) | 32.6667 |

SD(X) | 1.7078 |

SD(Y) | 6.7987 |

b | 3.2571 |

a | 21.2667 |

**The** correlation coefficient for the data = r =
0.8182

Predicted = 21.2667 + 5 * 3.2571 = 37.5522

Actual = 33

The residual value for *x* = 5. is ,

= 33 - 37.5522

= -4.5522

Consider the following small data set.
Subject
x
y
1
15
31
2
7
19
3
10
25
4
4
28
5
5
31
Find the linear correlation coefficient.
r=

Consider the following sample of 8 observations on X and Y:X: 4
19 2 17 16 20 7 20 Y: 25 22 19 14 3 4 20 9 (a) Determine the
coefficient of correlation between Y and X. (b) Determine the
coefficients (i.e., the a and b values) of the regression equation
Y = a + bX. (c) Interpret the values of the coefficients a and
b.

Here is a bivariate data set.
x
y
50
-36
17
129
39
58
19
91
31
84
45
22
18
80
30
92
8
175
Find the correlation coefficient and report it accurate to four
decimal places.
r =

Which of the following would be the LSRL for the given data?
x
2
7
8
11
17
16
y
23
28
29
40
28
42
a) ŷ = 23.53 + 0.8004 x
b) ŷ = 23.53 - 0.8004 x
c) ŷ = 0.8004 + 23.53 x
d) ŷ = 0.8004 - 23.53 x
e) None of the above

1. Given the following observations of quantitative variables
X and Y:
x= 0, 1, 2, 3, 15
y= 3, 4, 6, 10, 0
a. Make a scatterplot of the data on the axes. Circle the most
influential observation. (4 points)
(b) Determine the LSRL of Y on X. Draw
this line carefully on your scatterplot. (4 points)
(c) What is the definition of a regression outlier? (4
points)
(d) Which data point is the biggest regression outlier?
(4 points)...

Find regression line for the data
X 0 1 2 3
4 5 6 7
8
Y 11 21 31 41 51 61 71 81 91
X 0 2 4 6 8
10
Y 12 15 17 18 20 22

Given the following sample data set.
X= 2 3 5 6 6
Y= 10 9 7 4 2
a. Draw a scatter diagram of the data. (using Ti 84)
b. Compute the correlation coefficient r. Then use 0.05
significance level to test whether there is a linear correlation
between x and y. (using Ti 84)

4th Grade (Class 1)
4th Grade (Class 2)
12
10
15
12
21
16
21
17
22
17
22
19
22
19
25
22
26
22
27
22
27
27
31
28
32
29
33
29
33
31
36
31
37
31
38
33
41
33
43
37
44
39
45
43
45
43
47
47
55
49
57
57
The collected data is from two 4th grade (All female classes -
Age 10) Fitnessgram pacer tests. Once you have...

x
y
23
28
17
20
8
2
29
22
12
18
Use the sample data above to answer the following
question. (See exercise 56 on page 160 of your textbook
for a similar problem.)
Compute the correlation.

Use the given data to compute parts (a) and (b) below. X is 2.2,
4, 3, 4.6 and Y is 4, 1.4, 3.6, 4.8
Compute the linear correlation coefficient. The linear
correlation coefficient for the four pieces of data is
?...…..(round to three decimal places)

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