Consider the following sample data: y 52 54 27 58 36 62 53 41 X1 50 48 34 56 24

Question

Consider the following sample data: y 52 54 27 58 36 62 53 41 X1 50 48 34 56 24 75 45 43 X2 26 1 6 24 29 27 23 Click here for the Excel Data File a-1. Estimate a multiple linear regression model. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) y-hat a-2. Interpret its coefficients x1 O As x1 increases by one unit, y is predicted to increase by 0.68 units, holding x2 constant. OAs x1 increases by one unit, y is predicted to increase by 18.18 units, holding x2 constant. O As x1 increases by one unit, y is predicted to decrease by 0.68 units, holding x2 constant. As x increases by one unit, y is predicted to decrease by 18.18 units, holding x2 constant. a-3. Interpret its coefficients x2 O As x2 increases by one unit, y is predicted to decrease by 18.18 units, holding x1 constant. O As x2 increases by one unit, y is predicted to increase by 18.18 units, holding x1 constant. O As x2 increases by one unit, y is predicted to increase by 0.1 units, holding x1 constant. As x2 increases by one unit, y is predicted to decrease by 0.1 units, holding x1 constant. b. Find the predicted value for y if x equals 50 and x2 equals 20. (Round the intermediate calculations and final answer to 2 decimal places.) y-hat

Explanation / Answer

The statistical software output for this problem is:

Multiple linear regression results:
Dependent Variable: y
Independent Variable(s): x1, x2
y = 18.180651 + 0.67787327 x1 + -0.095676349 x2

Parameter estimates:

Analysis of variance table for multiple regression model:

Summary of fit:
Root MSE: 7.6152436
R-squared: 0.712
R-squared (adjusted): 0.5968

Hence,

Regression equation:

y - hat = 18.18 + 0.68 x1 + (-0.10) x2

Interpretation of coefficient x1: Option A is correct.

Interpretation of coefficient x2: Option D is correct.

For x1 = 50, x2 = 20

y - hat = 18.18 + 0.68 (50) + (-0.10) (20)

y - hat = 50.18

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 18.180651 12.604233 0 5 1.4424243 0.2088 x1 0.67787327 0.19500664 0 5 3.4761547 0.0177 x2 -0.095676349 0.47585908 0 5 -0.20106026 0.8486

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