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The relationship between yield of maize (a type of com), date of planting, and planting density was investigated in the article “Development of a Model for Use in Maize Replant Decisions” (Agronomy Journal [1980]: 459-464). Let
y = Maize yield (percent)
x1 = Planting date (days after April 20)
x2 = Planting density (10.000 plants/ha)
The regression model with both quadratic terms (y = α + β1x1 + β2x2 + β3x3 + β4x4 + e where x3 =
- a. If α = 21.09, β1 = 0.653, β2 = 0.0022, β3 = 2.0206, and β4 = 0.4, what is the population regression
function ? - b. Use the regression function in Part (a) to determine the mean yield for a plot planted on May 6 with a density of 41,180 plants/ha.
- c. Would the mean yield be higher for a planting date of May 6 or May 22 (for the same density)?
- d. Is it appropriate to interpret β1 = 0.653 as the average change in yield when planting date increases by one day and the values of the other three predictors are held fixed? Why or why not?
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Chapter 14 Solutions
Introduction to Statistics and Data Analysis
- If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardWhat is regression analysis? Describe the process of performing regression analysis on a graphing utility.arrow_forward
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