Use the following linear regression equation to answer the questions. x3 =-17.8

Question

Use the following linear regression equation to answer the questions. x3 =-17.8 + 4.2x1 + 9.8x4-1.0x7 (a) Which variable is the response variable? xs x7 Which variables are the explanatory variables? (Select all that apply.) X7 x4 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X1 coefficient x4 coefficient xy coefficient (c) If X1 5, x4 =-1, and x7 = 2, what is the predicted value for x)? (Round your answer to one decimal place.) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope. O If we look at all coefficients together, each one can be thought of as a "slope." O If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope. O If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line. Suppose x1 and x7 were held at fixed but arbitrary values. If x4 increased by 1 unit, what would we expect the corresponding change in x to be? 11x4 increased by 3 units, what would be the corresponding expected change in x)? If x4 decreased by 2 units, what would we expect for the corresponding change in x? (e) Suppose that n 18 data points were used to construct the given regression equation and that the standard error for the coefficient of K4 0.994. Construct a 90% confidence interval for the coefficient of x4. (Round your answers to two decimal places.) lower limit upper limit

Explanation / Answer

a)
x3 is the response variable. this is also called as dependent variable

x1, x4 and x7 are explanatory variable. this is also called as independent variable.

b)
constant = -17.8
x1 coeff = 4.2
x4 coeeff 9.8
x7 coeff -1

c)
x3 = -17.8 + 4.2*5 + 9.8*(-1) - 1*2
x3 = -8.6

d)
If we hold all other explanatory variables as fixed constants, then we can look at one coefficient at slope.

If x4 increased by 1 unit, change in x3 to be 9.8
If x4 increased by 3 unit, change in x3 to be 9.8*3 = 29.4
If x4 decreased by 2 unit, change in x3 to be 9.8*2 = 19.6

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