Free response · Unit 5 Beta

Coffee shop seats and revenue: reading regression output

Q2: Analyze and interpret data · calculator allowed · 10 points

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The question

Name: ______________________   Date: ____________   Coffee shop seats and revenue: reading regression output (10 points)

Graph

Seats and weekly revenue at 15 coffee shops

A coffee chain records the number of seats and the weekly revenue (thousands of dollars) at 15 of its shops. The scatterplot and part of the regression output are below. (Invented data.)
Regression of weekly revenue (thousands of dollars) on number of seats
PredictorCoef
Constant4.102
Seats0.3121
S = 0.726R-Sq = 96.3%
1020304050101520number of seatsweekly revenue ($1,000)

  1. (a) Describe the relationship between number of seats and weekly revenue shown in the scatterplot. [2 points]

  2. (b) Write the equation of the least-squares regression line, defining any variables you use, and interpret its slope in context. [2 points]

  3. (c) One shop has 30 seats and weekly revenue of 15.1 thousand dollars. Calculate and interpret its residual. [2 points]

  4. (d) Interpret the values of R-Sq and S in context. [2 points]

  5. (e) The chain is planning a shop with 85 seats. Explain why using the line to predict its weekly revenue could be unreliable. [1 point]

  6. (f) Suppose a 16th shop with 85 seats and weekly revenue of 21.0 thousand dollars were added to the data. Explain how this point would affect the least-squares slope, and identify what kind of point it is. [1 point]