Question

Marketing researchers were interested in how our perception of a food container’s volume is affected by the shape(as measured by surface area) of a container. The article “Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach?” (Journal of Marketing Research [1999]:313-326) gave data on the dimensions of 27 representative food items (e.g. San Miguel beer, Planters cheese balls, Gerber baby food and so on). Summary statistics for two variables (surface area and volume) are provided: Descriptive Statistics: surface area, volume Variable Mean StDev Minimum Q1 Median Q3 Maximum surface area (cm2) 45.69 39.31 16.32 23.77 33.8 48.06 174.42 volume (ml) 463.5 474.5 90.0 200.0 310.0 570.0 2330.0 Correlations: surface area, volume Pearson correlation of surface area and volume = 0.892

a) Find the least squares regression line of volume on surface area. Show all your work and circle the final regression equation. In your calculations, carry as many decimal places as your calculator can handle in the computation. Round your final answer to two decimal places.

b) Explain in simple language what the slope of this line tells you about the relationship between the two variables in the context of this problem. Be specific.

c) Find and interpret the value of R2 in context. What does this suggest about our ability to assess volume from a container’s surface area?

Answer 1