MKC2500 Lecture Notes - Lecture 15: Laundry Detergent, Linear Regression, Confidence Interval
18 Jun 2018
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ETC2500 Notes
Regression in SPSS example
The expected relationship between x = age (in years) and y = price (in dollars) is
estimated as
price = 4.147 – 0.016 x age (We know this relationship is not perfect)
• The estimated intercept term for the regression equation is 4.147, and the
corresponding 95% confidence interval is given by [3.663, 4.631] cents
• The estimated slope term for the regression equation is 0.016, and the
corresponding 95% confidence interval is given by [-2.6, -0.3] cents
• Since both the 95% CIs do not contain zero, we can say both estimated
coefficients are significantly different from zero
Interpretation
• The youngest age reported in this sample is 17 years.
• The (estimated) expected price when x = 17 is price = 4.1470.016(17) = 3.875
or $3.88.
• For each additional year in age, we expect a decrease of 1.6 cents (=$0.016),
on average, in the price paid by consumers for laundry detergent.
• A better way to say this might be that, for each additional 10 years in age, we
expect a decrease of 16 cents (=101.6), on average, in the price paid by
consumers for laundry detergent.
Regression with a dummy variable
• There is a connection between parametric ANOVA and Regression
• (Beyond the use of the ANOVA table to summarise the regression t
information)
• A dummy variable is a binary variable that takes on the values of zero and
one, only:
So testing
H0 : β1 = 0 vs H1 : β1 ≠ 0 (Regression) is equivalent to testing H0: µ1 = µ0 vs. H0 : µ1 ≠
µ0 (ANOVA)
