QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
17. SSE can never be
a. larger than SST
b. smaller than SST
c. equal to 1
d. equal to zero
18. A regression analysis between sales (in $\$ 1000$ ) and price (in dollars) resulted in the following equation
$\bar{Y}= 50,000 - 8 X$
The above equation implies that an
a. increase of $\$ 1$ in price is associated with a decrease of $\$ 8$ in sales
b. increase of $\$ 8$ in price is associated with an increase of $\$ 8,000$ in sales
c. increase of $\$ 1$ in price is associated with a decrease of $\$ 42,000$ in sales
d. increase of $\$ 1$ in price is associated with a decrease of $\$ 8000$ in sales
# Exhibit 12 - 6
| | | |
| --- | --- | --- |
| Dependent Variable | | Independent Variable |
| 20 | | 3 |
| 25 | | 5 |
| 32 | | 8 |
| 43 | | 12 |
19. Refer to Exhibit 12 - 6. The slope of the regression equation is a. 120.348 b. 12.1965 c. - 2.5435 d. 2.5435
20. Refer to Exhibit 12 - 6. The $y$ intercept is a. 120.348 b. 12.1965 c. - 2.5435 d. 2.5435
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Answer
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Step 1I'll solve these problems step by step, following the precise LaTeX formatting guidelines:
Problem 17: SSE (Sum of Squared Errors) Relationship
Step 2: Understand SSE and SST
- SST (Total Sum of Squares) represents total variance in the dependent variable - SSE (Sum of Squared Errors) represents unexplained variance
Final Answer
Problem 18: Regression Equation Analysis Step 1: Interpret the Equation \bar{Y} = 50,000 - 8X - \bar{Y} represents predicted sales - For each $\$1$ increase in price (X), sales decrease by $\$8$ Step 2: Calculation Example - If price increases by $\$1$, sales will decrease by $\$8$ Problem 19: Slope Calculation Step 1: Slope Formula \text{Slope} = \frac{n\sum{xy} - \sum{x}\sum{y}}{n\sum{x^{2}} - (\sum{x})^{2}} Step 2: Calculate Components - \sum{x} = 3 + 5 + 8 + 12 = 28 - \sum{y} = 20 + 25 + 32 + 43 = 120 - \sum{xy} = (3 \times 20) + (5 \times 25) + (8 \times 32) + (12 \times 43) Step 3: Detailed Calculation - After careful computation, the slope is 2.5435 Problem 20: Y-Intercept Calculation Step 1: Y-Intercept Formula b_{0} = \bar{y} - b_{1}\bar{x} Step 2: Calculate Mean Values - \bar{x} = \frac{28}{4} = 7 - \bar{y} = \frac{120}{4} = 30 Step 3: Use Slope from Previous Problem - Slope b_{1} = 2.5435 - b_{0} = 30 - (2.5435 \times 7) = 12.1965
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