Concept explainers
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
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- The authors of the paper "Power-Load Prediction Based on Multiple Linear Regression Model"t were interested in predicting the load on the electric power system in China using data on y = Power consumption (in hundreds of millions of kwh), x, Population (in millions), and x, = Gross domestic %3D product (in billions of dollars), for 21 years. The model equation proposed in the paper is y = -113,527 + 0.974x, + 0.057x, + e. (a) According to this model, what is the mean power consumption (in hundreds of millions of kwh) for a year if the population was 160,000 million and the gross domestic product was 600,000 billion dollars? hundreds of millions of kwh (b) Interpret the value of B, in this model. When the [ gross domestic product v is fixed, the mean increase in [power consumption (in hundreds of millions of kwh) V associated with a 1-million unit increase in [population is 0.974.arrow_forwardIs there a relation between the age difference between husband/wives and the percent of a country that is literate? Researchers found the least-squares regression between age difference (husband age minus wife age), y, and literacy rate (percent of the population that is literate), x, is y = - 0.0432x+ 8.3. The model applied for 16arrow_forwardA sample consists of 500 houses sold in Karachi between Jamuary 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. (300 words) Table: Coefficients Model Unstandardized Coefficients VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area p.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90 R? = 0.67; DW = 2.08 Dependent Variable: House price (Pakistani rupees in Million) a) You are required to write the multiple regression equation. b) How would you interpret the above Output' of a regression analysis performed in SPSS? c) From the above results, what can you say about the nature of autocorrelation? d) Is there multicollinearity in regression? How do you know?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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