Question

A statistical program is recommended.

Consider the following data for a dependent variable *y*
and two independent variables,

x_{1}

and

x_{2}.

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

30 | 12 | 94 |

47 | 10 | 108 |

25 | 17 | 112 |

51 | 16 | 178 |

40 | 5 | 94 |

51 | 19 | 175 |

74 | 7 | 170 |

36 | 12 | 117 |

59 | 13 | 142 |

76 | 16 | 211 |

(a)

Develop an estimated regression equation relating *y*
to

x_{1}.

(Round your numerical values to one decimal place.)ŷ =

Predict *y* if

x_{1} = 51.

(Round your answer to one decimal place.)

(b)

Develop an estimated regression equation relating *y*
to

x_{2}.

(Round your numerical values to one decimal place.)ŷ =

Predict *y* if

x_{2} = 16.

(Round your answer to one decimal place.)

(c)

Develop an estimated regression equation relating *y*
to

x_{1} and x_{2}.

(Round your numerical values to one decimal place.)ŷ =

Predict *y* if

x_{1} = 51

and

x_{2} = 16.

(Round your answer to one decimal place.)

Answer #1

Using Excel, go to Data, select Data Analysis, choose Regression. Put y in Y input range and put x1, x2 and then x1 and x2 in X input range seperately and run 3 seperate models.

a) x1

Coefficients | Standard Error | t Stat | P-value | |

Intercept | 51.53 | 18.14 | 2.84 | 0.02 |

x1 | -0.21 | 1.35 | -0.15 | 0.88 |

y = 51.53 - 0.21x1

x_{1} = 51, y = 51.53 - 0.21*51 = 40.8

b) x2

Coefficients | Standard Error | t Stat | P-value | |

Intercept | 1.32 | 12.53 | 0.11 | 0.92 |

x2 | 0.34 | 0.09 | 3.94 | 0.00 |

y = 1.32 - 0.34x_{2}

x_{2} = 16, y = 1.32 - 0.34*16 = -4.1

c) x1 and x2

Coefficients | Standard Error | t Stat | P-value | |

Intercept | 13.19 | 7.63 | 1.73 | 0.13 |

x1 | -2.15 | 0.51 | -4.24 | 0.00 |

x2 | 0.45 | 0.06 | 8.13 | 0.00 |

y = 13.19 - 2.15x_{1} + 0.45x_{2}

x_{1} = 51 and x_{2} = 16, 13.19 - 2.15*51+
0.45*16 = 13.19 - 116.85 = -103.66

8. Consider the following data for a dependent variable
y and two independent variables, x1 and
x2.
x1
x2
y
30
12
94
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
(a) Develop an estimated regression equation relating y
to x1. (Round your numerical values to one decimal
place.)
ŷ = ______
Predict y if x1 = 51. (Round
your answer...

A statistical program is recommended.
Consider the following data for a dependent variable y
and two independent variables,
x1
and
x2.
x1
x2
y
30
12
94
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
The estimated regression equation for the data is
ŷ = −18.4 + 2.01x1 + 4.74x2.
(a)
Develop a 95% confidence interval for the mean value of...

Consider the following data for a dependent variable y and two
independent variables, x1 and x2 . x 1 x 2 y 29 13 94 46 11 109 25
17 112 50 16 178 40 6 95 51 19 175 74 7 170 36 13 117 59 13 143 76
17 212 Round your all answers to two decimal places. Enter negative
values as negative numbers, if necessary. a. Develop an estimated
regression equation relating y to x1 . ŷ...

Consider the following data for a dependent variable y and two
independent variables, x1 and x2.
x1
x2
y
29
12
95
46
10
109
24
17
113
50
17
178
40
5
94
52
19
176
74
7
170
36
13
118
59
13
143
76
16
212
Round your all answers to two decimal places. Enter negative
values as negative numbers, if necessary.
a. Develop an estimated regression equation
relating y to x1.
y^=_____ + _____x1 (fill in...

Consider the following data for a dependent variable y
and two independent
variables, x1 and
x2.
x1
x2
y
30
12
94
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
The estimated regression equation for these data isŷ =
−18.37 + 2.01x1 +
4.74x2.
Here, SST = 15,182.9, SSR = 14,052.2,
sb1 =
0.2471, and sb2
= 0.9484.
(A) Test for a significant relationship...

You may need to use the appropriate technology to answer this
question.
Consider the following data for a dependent variable y
and two independent variables, x1 and
x2.
x1
x2
y
30
12
95
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
The estimated regression equation for these data is
ŷ = −17.85 + 2.00x1 +
4.73x2.
Here, SST = 15,091.6,...

Consider the following data for a dependent variable y
and two independent variables, x1and
x2.
x1
x2
y
30
12
96
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
The estimated regression equation for these data is ŷ =
−17.33 + 2.00x1 +
4.73x2.
Here, SST = 15,002.1, SSR = 13,887.5,
sb1 =
0.2454,and
sb2 =
0.9417.
(a)Test for a significant...

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...

The owner of Showtime Movie Theaters, Inc., would like to
predict weekly gross revenue as a function of advertising
expenditures. Historical data for a sample of eight weeks
follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5.0
1.5
90
2.0
2.0
95
4.0
1.5
92
2.5
2.5
95
3.0
3.3
94
3.5
2.3
94
2.5
4.2
94
3.0
2.5
(a)
Develop an estimated regression equation with the amount of
television advertising as the independent variable. (Round...

Data for two variables, x and y, follow.
xi
1 2 3 4 5
yi
5 9 7 13 16
(a)
Develop the estimated regression equation for these data. (Round
your numerical values to two decimal places.)
ŷ = 2.20+2.60x
Compute the studentized deleted residuals for these data. (Round
your answers to two decimal places.)
xi
yi
Studentized
Deleted Residual
1
5
2
9
3
7
4
13
5
16

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 5 minutes ago

asked 6 minutes ago

asked 24 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago