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Chapter 4: Q. 4.2 (page 160)
Fill in the blank.
The graph of a linear equation with one independent variable is a _____.
The graph of a linear equation with one independent variable is a straight line.
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A measure of the total variation in the observed values of the response variable is the------.
The mathematical abbreviation for it is----.
Fill in the blanks.
a. In the context of regression, an_______ is a data point that lies far from the regression line, relative to the other data points.
b. In regression analysis, an_______ is a data point where removal causes the regression equation to change considerably:
Corvette Prices. Following are the age and price data for Corvettes from Exercise :
a. Compute SST,SSR,SSE
b. Compute the coefficient of determination
c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer.
d. State how useful the regression equation appears to be for making predictions.
Road Grade. The grade of a road is defined as the distance it rises (or falls) to the distance it runs horizontally, usually expressed as a percentage. Consider a road with a positive grade, . Suppose that you begin driving on that road at an altitude
a. Find the linear equation that expresses the altitude, , when you have driven a distance, ,along the road. (Hint: Draw a graph and apply the Pythagorean Theorem
b. Identify and interpret the -intercept and slope of the linear equation in part (a).
c. Apply your results in parts (a) and (b) to a road with a grade and an initial altitude of . Express your answer for the slope to four decimal places.
d. For the road in part (c). what altitude will you reach after driving along the road?
e. For the road in part (c), how far along the road must you drive to reach an altitude of ?
Plant Emissions. Plants emit gases that trigger the ripening of fruit, attract pollinators, and cue other physiological responses. N. Agelopolous et al. examined factors that affect the emission of volatile compounds by the potato plant Solanum numerous and published their findings in the paper "Factors Affecting Volatile Emissions of Intact Potato Plants. Solanum tuberosum: Variability of Quantities and Stability of Ratios" (Journal of Chemical Ecology, Vol. 26. No. 2, pp. 497-511). The volatile compounds analyzed were hydrocarbons used by other plants and animals. Following are data on plant weight (x), in grams, and quantity of volatile compounds emitted (y), in hundreds of nanograms, for 11 potato plants. For part (g), predict the number of volatile compounds emitted by a potato plant that weighs 75 grams.
| X | 57 | 85 | 57 | 65 | 52 | 67 | 62 | 80 | 77 | 53 | 68 |
| Y | 8.0 | 22.0 | 10.5 | 22.5 | 12.0 | 11.5 | 7.5 | 13.0 | 16.5 | 21..0 | 12.0 |
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