Statistics

 

Construct a scatter plot in Excel with Age as the independent variable and Assessment Value as the dependent variable. Insert the bivariate linear regression equation and r^2 in your graph. Do you observe a linear relationship between the 2 variables?

Use Excel’s Analysis Tool Pak to conduct a regression analysis of Age and Assessment Value. Is Age a significant predictor of Assessment Value?

Construct a multiple regression model.

Use Excel’s Analysis Tool Pak to conduct a regression analysis with Assessment Value as the dependent variable and Floor Area, Offices, Entrances, and Age as independent variables. What is the overall fit r^2? What is the adjusted r^2?
Which predictors are considered significant if we work with α=0.05? Which predictors can be eliminated?
What is the final model if we only use Floor Area and Offices as predictors?
Suppose our final model is:
Assessed Value = 115.9 + 0.26 x FloorArea + 78.34 x Offices
What would be the assessed value of a medical office building with a floor area of 3500 sq. ft., 2 offices, that was built 15 years ago? Is this assessed value consistent with what appears in the database?

Sample Solution

Bumble bees play a major part in many of the world’s ecosystems; providing a reproduction medium for many species of flowering plants and agricultural crops, and playing the role of a food source for many species of bats and birds (Cameron et al., 2010). The population of bumble bees has been trending down for some years now, giving rise to many ecological concerns about how the populations can be conserved. Without the bumble bee, the world’s food chains could become severely compromised. The populations of many producer species would decline due to the lack of a major reproduction medium, consequently resulting in the decrease in population of primary consumers, secondary consumers, and tertiary consumers. As the minimum temperature of alpine climates increase, the density of mutualistic plant species in said region begins to decline, resulting in higher competition between alpine bumble bee species for resources (Miller-Struttman et al. 2015). The purpose of Miller-Struttman et al.’s article, entitled Functional mismatch in a bumble bee pollination mutualism under climate change, is to examine the affects that climate change has had on the populations of bumble bee species. Specifically, the Miller-Struttman et al.’s article examines the affect that climate change has had on the mutualistic relationships between bumble bee species, and their corresponding host plant species. Bumble bees are equipped with a tongue (proboscis) that they use to drink nectar from the tubes of plants. In turn, the bumble bee picks up some of the plant’s pollen, and transports it, increasing the likelihood that said plant will reproduce. The overall purpose of Miller-Struttman et al.’s experiment is to examine the affects that climate change has had (if any) on the physical structures (proboscises and nectar tubes), and to determine if said changes will have an affect on the population of bee species. Figure 1.1 below details the experiment’s hypothesis, independent variables, and dependent variables.

Hypothesis

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