Question

In: Economics

The following table gives the price (in dollars), weight (in pounds), amps, and maximum cutting depth...

The following table gives the price (in dollars), weight (in pounds), amps, and maximum cutting depth (in inches) for a collection of 19 circular saws.

Price Weight Amps Depth

150

 11 15 2.4
110 12 15 2.2
130 11 15 2.4
150 11 15 2.3
140 12 15 2.4
100 11 15 2.4
150 13 15 2.5
90 9 10 2.5
140 11 15 2.4
110 12 15 2.4
70 12 14 2.4
30 10 10 2.5
80 12 13 2.4
50 11 13 2.4
80 13 14 2.4
30 10 12 2.5
50 11 12 2.5
45 11 12 2.5
40 10 12 2.4

1.Make a prediction about the impact of each independent variable on the dependent variable.

2.Use graphical summaries to examine the relationship between each pair of variables. What do you see? Are there any unusual observations or outliers? Does the data support your predictions?

3.Write the regression equation.

4. Estimate the regression model. Interpret the estimated coefficients.

5. Predict the price of a circular saw that weighs 10 pounds, uses 12 amps of current, and has a maximum cutting depth of 2.5 inches.

6. Describe the fit of the model.

7. Find the residuals for the regression.

8. Test whether or not the coefficients are jointly significant. Be sure to set up the hypothesis, the decision rule, and the conclusion.

9.Test whether or not the price is significantly impacted by amps. Be sure to set up the hypothesis, the decision rule, and the conclusion.

Solutions

Expert Solution

Price Weight Amps Depth
150 11 15 2.4
110 12 15 2.2
130 11 15 2.4
150 11 15 2.3
140 12 15 2.4
100 11 15 2.4
150 13 15 2.5
90 9 10 2.5
140 11 15 2.4
110 12 15 2.4
70 12 14 2.4
30 10 10 2.5
80 12 13 2.4
50 11 13 2.4
80 13 14 2.4
30 10 12 2.5
50 11 12 2.5
45 11 12 2.5
40 10 12 2.4
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.809847
R Square 0.655852
Adjusted R Square 0.587022
Standard Error 27.83118
Observations 19
ANOVA
df SS MS F Significance F
Regression 3 22141.91 7380.637 9.528636 0.000907
Residual 15 11618.62 774.5744
Total 18 33760.53
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -303.445 304.189 -0.99756 0.334316 -951.809 344.918 -951.809 344.918
Weight -10.808 8.721448 -1.23925 0.234294 -29.3974 7.781292 -29.3974 7.781292
Amps 25.674 6.13971 4.181631 0.000802 12.58752 38.76048 12.58752 38.76048
Depth 70.02956 109.1225 0.641752 0.53072 -162.56 302.6187 -162.56 302.6187
RESIDUAL OUTPUT
Observation Predicted Price Residuals
1 130.8471 19.15288
2 106.0332 3.966826
3 130.8471 -0.84712
4 123.8442 26.15584
5 120.0391 19.96091
6 130.8471 -30.8471
7 116.234 33.76599
8 31.09614 58.90386
9 130.8471 9.15288
10 120.0391 -10.0391
11 94.36509 -24.3651
12 20.28811 9.711894
13 68.69109 11.30891
14 79.49912 -29.4991
15 83.55705 -3.55705
16 71.63611 -41.6361
17 60.82807 -10.8281
18 60.82807 -15.8281
19 64.63315 -24.6332

3. Price = -303.45 - 10.81*Weight + 25.67*Amps + 70.03*Depth

4. Price = -303.45 - 10.81*Weight + 25.67*Amps + 70.03*Depth + u

Interpretation of the estimated coefficients:

As Weight increases by a pound, price of a circular saw decreases by 10.81 dollars, other factors constant.

A unit increase in Amps leads to increase in price of a circular saw by 25.67 dollars, other factors constant.

As Depth increases by an inch, price of a circular saw increases by 70.03 dollars, other factors constant.

5. price of a circular saw that weighs 10 pounds, uses 12 amps of current, and has a maximum cutting depth of 2.5 inches

Price = -303.45 - 10.81*10 + 25.67*12 + 70.03*2.5

= -303.45 - 108.1 + 308.04 + 175.075

= 71.565

=72 dollars

6. R-squared = 0.66

i.e. 68% of the variability around the mean is explained by this model.

7.

Residuals
19.15288
3.966826
-0.84712
26.15584
19.96091
-30.8471
33.76599
58.90386
9.15288
-10.0391
-24.3651
9.711894
11.30891
-29.4991
-3.55705
-41.6361
-10.8281
-15.8281

-24.6332

Note: max. 4 parts at a time

Rahul Sunny answered 2 years ago
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