1) Consider the first-order model yˆ = 70 + 35×1 – 10×2 + 5x1x2. A unit increase in x2, while holding x1 constant at 1, changes the value of E(y) by:
Suppose at first
2) For the multiple regression model Yˆ = 50 + 25×1 – 10×2 + 8×3, if x2 were to increase by 5, holding x1 and x3 constant, the value of y would:
3) In a laboratory experiment, data were gathered on the life span (Y in months) of 33 rats, units of daily protein intake (X1), and whether or not agent X2 (a proposed life extending agent) was added to the rats diet (X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
Yˆ=36+0.8X1−1.7X2
Also provided are SSR = 60 and SST = 180.
If we want to test for the significance of the model, the critical value of F at 95% confidence is
4) In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is
5) In a laboratory experiment, data were gathered on the life span (Y in months) of 33 rats, units of daily protein intake (X1), and whether or not agent X2 (a proposed life extending agent) was added to the rats diet (X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
Yˆ=36+0.8X1−1.7X2
Also provided are SSR = 60 and SST = 180.
The life expectancy of a rat that was given 3 units of protein daily, and who took agent X2 is
6) In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are
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