Question
In: Statistics and Probability
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between advertising budget and sales for Product A:
| Observation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Advertising ($) | 60,000 | 70,000 | 70,000 | 80,000 | 80,000 | 90,000 | 100,000 | 100,000 | 110,000 | 110,000 |
| Sales ($) | 363,000 | 432,000 | 417,000 | 502,000 | 483,000 | 537,000 | 614,000 | 625,000 | 653,000 | 666,000 |
What is the slope of the "least-squares" best-fit regression line?
Solutions
Expert Solution
| X | Y | XY | X² | Y² |
| 60000 | 363000 | 21780000000 | 3600000000 | 1.31769E+11 |
| 70000 | 432000 | 30240000000 | 4900000000 | 1.86624E+11 |
| 70000 | 417000 | 29190000000 | 4900000000 | 1.73889E+11 |
| 80000 | 502000 | 40160000000 | 6400000000 | 2.52004E+11 |
| 80000 | 483000 | 38640000000 | 6400000000 | 2.33289E+11 |
| 90000 | 537000 | 48330000000 | 8100000000 | 2.88369E+11 |
| 100000 | 614000 | 61400000000 | 10000000000 | 3.76996E+11 |
| 100000 | 625000 | 62500000000 | 10000000000 | 3.90625E+11 |
| 110000 | 653000 | 71830000000 | 12100000000 | 4.26409E+11 |
| 110000 | 666000 | 73260000000 | 12100000000 | 4.43556E+11 |
| Ʃx = | Ʃy = | Ʃxy = | Ʃx² = | Ʃy² = |
| 870000 | 5292000 | 4.7733E+11 | 78500000000 | 2.90353E+12 |
| Sample size, n = | 10 |
| x̅ = Ʃx/n = | 87000 |
| y̅ = Ʃy/n = | 529200 |
| SSxx = Ʃx² - (Ʃx)²/n = | 2810000000 |
| SSyy = Ʃy² - (Ʃy)²/n = | 1.03004E+11 |
| SSxy = Ʃxy - (Ʃx)(Ʃy)/n = | 16926000000 |
Slope, b = SSxy/SSxx = 6.0234875
y-intercept, a = y̅ -b* x̅ = 5156.58363
Regression equation :
ŷ = 5156.5836 + (6.0235) x
orchestra answered 2 years agoRelated Solutions
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A:
Observation
1
2
3
4
5
6
7
8
9
10
Advertising ($)
50,000
60,000
60,000
70,000
70,000
80,000
90,000
90,000
100,000
110,000
Sales ($)
299,001
371,000
364,000
430,000
440,000
485,000
535,000
546,000
595,000
675,000
What is the predicted sales quantity for an advertising
budget of $76,000?
Please round your answer to the nearest integer.
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A:
Observation
1
2
3
4
5
6
7
8
9
10
Advertising ($)
50,000
60,000
60,000
70,000
70,000
80,000
90,000
90,000
100,000
110,000
Sales ($)
299,001
371,000
364,000
430,000
440,000
485,000
535,000
546,000
595,000
675,000
What is the correlation value for the relationship
between advertising and sales?
Please round your answer to the nearest hundredth.
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A:
Observation
1
2
3
4
5
6
7
8
9
10
Advertising ($)
50,000
60,000
60,000
70,000
70,000
80,000
90,000
90,000
100,000
110,000
Sales ($)
299,001
371,000
364,000
430,000
440,000
485,000
535,000
546,000
595,000
675,000
What is the predicted sales quantity for an advertising
budget of $76,000?
Please round your answer to the nearest integer.
Note that the correct answer will be evaluated based...
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A:
Observation
1
2
3
4
5
6
7
8
9
10
Advertising ($)
100,000
110,000
110,000
120,000
130,000
130,000
140,000
150,000
150,000
160,000
Sales ($)
603,000
676,000
655,000
748,000
796,000
785,000
858,000
891,000
935,000
980,000
What is the slope of the "least-squares" best-fit
regression line?
Please round your answer to the nearest hundredth.
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A:
Observation
1
2
3
4
5
6
7
8
9
10
Advertising ($)
50,000
60,000
60,000
70,000
70,000
80,000
90,000
90,000
100,000
110,000
Sales ($)
299,001
371,000
364,000
430,000
440,000
485,000
535,000
546,000
595,000
675,000
What is the correlation value for the relationship
between advertising and sales?
Please round your answer to the nearest hundredth.
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A:
Observation
1
2
3
4
5
6
7
8
9
10
Advertising ($)
80,000
80,000
90,000
100,000
100,000
110,000
120,000
120,000
130,000
140,000
Sales ($)
499,000
477,000
546,000
614,000
623,000
653,000
747,000
714,000
785,000
858,000
What is the slope of the "least-squares" best-fit
regression line?
Please round your answer to the nearest hundredth.
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A:
Observation
1
2
3
4
5
6
7
8
9
10
Advertising ($)
50,000
60,000
60,000
70,000
70,000
80,000
90,000
90,000
100,000
110,000
Sales ($)
299,001
371,000
364,000
430,000
440,000
485,000
535,000
546,000
595,000
675,000
What is the slope of the "least-squares" best-fit
regression line?
Please round your answer to the nearest hundredth.
Note that the correct answer will be evaluated based on the...
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for
Product A: Observation 1 2 3 4 5 6 7 8 9 10
Advertising ($) 100,000 110,000 110,000 120,000 130,000 130,000
140,000 150,000 150,000 160,000
Sales ($) 603,000 676,000 655,000 748,000 796,000 785,000
858,000 891,000 935,000 980,000
What is the correlation value for the relationship between
advertising and sales?
Please round your answer to the nearest hundredth. Note that the
correct answer will be evaluated based...
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A:
Observation
1
2
3
4
5
6
7
8
9
10
Advertising ($)
100,000
110,000
110,000
120,000
130,000
130,000
140,000
150,000
150,000
160,000
Sales ($)
603,000
676,000
655,000
748,000
796,000
785,000
858,000
891,000
935,000
980,000
What is the slope of the "least-squares" best-fit
regression line?
Please round your answer to the nearest hundredth.
Consider the following sample data for the relationship between advertising budget and sales for Product A:...
Consider the following sample data for the relationship between
advertising budget and sales for Product A: Observation 1 2 3 4 5 6
7 8 9 10 Advertising ($) 90,000 100,000 100,000 110,000 120,000
120,000 130,000 140,000 140,000 150,000 Sales ($) 535,000 626,000
625,000 674,000 712,000 725,000 809,000 832,000 845,000 919,000
What is the predicted sales quantity for an advertising budget of
$119,000? Please round your answer to the nearest integer.
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