Question

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)

r=

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

Use at least 3 decimal places. (Round if necessary)

P-value =

At the alpha = 0.05 significance level, is the correlation
significant?

- Yes, significant correlation
- No

Answer #1

The statistical software output for this problem is:

From above output:

y = -**0.727**x + (-**1.382**)

r = -**0.423**

P - value = **0.2572**

**No,** the correlation is not significant.

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...

Linear Regression
Use linear regression to find the equation for
the linear function that best fits this data. Round both numbers to
two decimal places. Write your final answer in a form of an
equation y=mx+by=mx+b
x
1
2
3
4
5
6
y
98
122
156
176
213
219

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 = ______

Use linear regression to find the equation for
the linear function that best fits this data. Round both numbers to
two decimal places. Write your final answer in a form of an
equation y=mx+by=mx+b
x
1
2
3
4
5
6
y
93
110
138
170
191
212

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^ =

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...

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

Consider a linear regression model where y represents
the response variable, x is a quantitative explanatory
variable, and d is a dummy variable. The model is
estimated as yˆy^ = 15.4 + 3.6x −
4.4d.
a. Interpret the dummy variable
coefficient.
Intercept shifts down by 4.4 units as d changes from 0
to 1.
Slope shifts down by 4.4 units as d changes from 0 to
1.
Intercept shifts up by 4.4 units as d changes from 0 to
1.
Slope shifts...

Compute the least-squares regression equation for the
given data set. Round the slope and
y
-intercept to at least four decimal places.
x
6
1
4
7
3
y
2
4
1
7
6
Regression line equation: y=?

Compute the least-squares regression equation for the given data
set. Round the slope and y -intercept to at least four decimal
places. x 5 4 2 6 3 y 4 5 1 3 6 Send data to Excel Regression line
equation: = y

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