Question

Linear Regression and Correlation.

x | y |
---|---|

3 | -3.26 |

4 | 2.72 |

5 | 1.2 |

6 | 1.88 |

7 | 0.16 |

8 | -5.66 |

9 | 3.02 |

10 | -6.7 |

11 | -3.92 |

12 | -5.34 |

Compute the equation of the linear regression line in the form y =
mx + b, where m is the slope and b is the intercept.

Use at least 3 decimal places.

y = x +

Compute the correlation coeficient for this data set. Use at least
3 decimal places.

r=

Compute the P-value (Use H_A: slope ≠ 0 for the alterantive
hypothesis.)

P-value =

At the 0.01 significance level, is the correlation significant?

- No
- Yes, significant correlation

Answer #1

The statistical software output for this problem is:

Hence,

Regression equation:

y = (-0.649) x + 3.278

r = -0.522

P-value = 0.1219

No, the correlation is not significant.

Linear Regression and Correlation.
x
y
3
-10.52
4
1.94
5
-2.7
6
-3.14
7
-9.18
8
-4.82
9
-12.26
10
-11.1
11
-6.44
Compute the equation of the linear regression line in the form y =
mx + b, where m is the slope and b is the intercept.
Use at least 3 decimal places. (Round if necessary)
y = x +
Compute the correlation coeficient for this data set. Use at least
3 decimal places. (Round if necessary)...

x
7
0
3
4
3
1
y
6
2
6
5
6
7
Assuming that the regression equation is y = 4.433 + 0.300x and
that the SSE = 12.6333, test to determine if the slope is not equal
to zero using alpha = 0.10
a) Test Statistic T = ______ (round to two decimal places)
b) Critical value(s) = _______, _______ (round to 3 decimal
places)
c) P-value = ______

Compute the linear correlation coefficient from the given table.
X 1 2 4 6 7 Y 17 13 9 6 4

x
1
2
3
4
5
6
y
1107
1711
2467
3886
5440
7993
Use linear regression to find the equation for the linear function
that best fits this data. Round to two decimal places.
ˆy^ =

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)

Compute the Pearson correlation for the following data.
X Y
7 3
3 1
6 5
4 4
5 2

Data Set:
x
y
0
4
2
2
2
0
5
-2
6
1
1. Find intercept b0
2. Find slope B1
3. Find the best fitted linear regression equation
4.Graph observations
5.Graph the linear equation on the same plot
6. Find the coefficient of Determination r²
7. Find the linear correlation coefficient r
8.Interpret r (the correlation between x & y)

Consider the following set of ordered pairs.
x 6 1 4 3 4 0
y 5 2 5 3 4 5
Assuming that the regression equation is y=3.375 + 0.208x and
that the SSE=6.9583, test to determine if the slope is not equal
to zero using α=0.10.
State the hypotheses. Choose the correct answer below.
A. H0: β ≠0 H1: β=0
B. H0: β=0 H1: β>0
C. H0: β=0 H1: β≠0
D. H0: β=0 H1: β<0
Calculate the test statistic....

Use the data set to find the following:
X Y
4 1
7 16
3 4
5 7
6 7
a) Compute SSRegression
b) Compute MSRegression
c) Compute the F ratio for the regression analysis
d) Compute the t ratio for the slope
e) Compute the t ratio for the intercept

pt1) For the given data set, the estimated regression equation
is
y
x
12
4
3
6
7
2
6
4
Furthermore, it was determined that SST = 42
Calculate the value of F-statistic for the test of
significance. Round your answer to four decimal
places.
pt2) For the previous problem, what is the corresponding
critical F value at α = 5%
significance?
Show your answer with three decimal places.
pt3)
Using the results of questions #3 and #4, state...

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