Unit 9: Inference for Quantitative Data: Slopes

A researcher studies the relationship between hours of sunlight per day ([math]) and tomato plant yield in pounds ([math]) for 15 randomly selected plots. Computer output: ```\nPredictor Coef SE Coef T P\nConstant -1.25 2.10

A study examines the relationship between a city's population density ([math], in thousands per sq mile) and average commute time ([math], in minutes) for 20 randomly selected US cities. Summary: [math], [math], [math], [math].

A student investigates whether study time ([math], hours per week) predicts GPA ([math]) for 25 college students. The regression analysis produces: ```\nPredictor Coef SE Coef T P\nConstant 1.85 0.32 5.78 <0.001\nStud

An analyst fits a regression of home price ([math], in [math]x[math]\hat{y} = 45 + 0.12x[math]R^2 = 0.78[math]b_1 = 0.12[math]SE_{b_1} = 0.015[math]1,200,000. After including this point: [math], [math], [math], [math].

A biologist models the relationship between tree diameter ([math], in cm) and height ([math], in meters) for a species of pine tree. From 40 randomly selected trees: [math], [math], [math], [math]. \nThe researcher wants to predict the height of a tr

Four residual plots are described below from different regression analyses (all with [math]): **Plot A:** Residuals randomly scattered, no pattern, constant spread. **Plot B:** Residuals show a clear curve (U-shape). **Plot C:** Residuals fan out — s

An economist models the relationship between years of education ([math]) and annual income ([math], in $1000s) for 50 randomly selected workers in a metropolitan area: ```\nPredictor Coef SE Coef T P\nConstant -12.5 8.3

A marketing analyst builds two models predicting weekly sales ([math]) for a retail chain: **Model 1:** [math] (advertising spend in [math]R^2 = 0.45[math]S = 42[math]t_{slope} = 4.2[math]p < 0.001[math]\hat{y} = 180 + 12x_1 + 8x_2[math]R^2 = 0.68[ma

A fitness researcher collects data on 12 adults, measuring their weekly exercise hours ([math]) and resting heart rate ([math], bpm): \nSummary statistics: [math], [math], [math], [math], [math].

A state environmental agency studies whether a factory's distance from a river ([math], miles) is related to the concentration of a pollutant in nearby groundwater ([math], ppm). Data from 18 monitoring wells: ```\nPredictor Coef SE Coef T