House prices How does the price of a house depend on its size? Data from Saratoga, New York, on 1064 randomly selected houses that had been sold include data on price ($1000s) and size (1000s ft2), producing the following graphs and computer output: Dependent variable is: Price R squared = 59.5% s = 53.79 with 1064 - 2 = 1062 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept -3.11686 4.688 -0.665 0.5063 Size 94.4539 2.393 39.5 0.0001 a) Explain in context what the regression says. b) The intercept is negative. Discuss its value, taking note of its P-value. c) The output reports s = 53.79. Explain what that means in this context. d) Whats the value of the standard error of the slope of the regression line? e) Explain what that means in this context.

QuadraticRelationship - Check the residual plot to determine of the form of model is appropriate QuadraticModel QuadraticModel(2) QuadraticModel NoteExample ConcaveUpward - As price increase the sales volume decrease at a decreasing rate b0= 539242.8 b1= -765344.8 b2= 290156.24 Interpretations b = 539242.8 0 We predicted the sales volume to be 539242.8 when the price of cat food is 0. - This is extrapolation b1= -765344.8 We have no potential interpretation - What if we increase x1 by 1 unit b 2 290156.24 Since b2 is positive, we have a positive concave upward relationship between price and volume of cat food. HypothesisTesting H 0β 20 vs H :a >2 t-test T = 20.23 p-value =