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Whether the following statement is true or not. Explain why.

Let Y be a random variable. Then var(Y) equals E [(Y − μY )] . ​

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Related questions

42) Suppose a firm is trying to decide whether or not to temporarily shut down to minimize total loss. If price equals average variable cost, then A) total variable cost equals total fixed cost. B) total revenue equals total variable cost, and the loss equals total fixed cost. C) total revenue equals total fixed cost, and the loss equals total variable cost. D) total cost equals total variable cost. E) total fixed cost is zero.

Monetary Policy and Inflation: Use our standard Keynesian macroeconomic model:

• Y = E = C + I + NX + G — GDP equals the sum of consumption, investment, net exports, and government purchases
• C = c0 + cy x Y — consumption equals the consumer-confidence term plus the mpc times GDP or income
• I = I0 - Ir x r — business investment spending equals the business animal-spirits term minus the interest sensitivity of investment times the long-run real risky interest rate
• μ = 1/(1 - cy) — the multiplier is the inverse of one minus the mic
• Y = μ(c0 + I0 + NX) - (μ Ir) x r + μG — our summing-up equation, telling us how the level of annual GDP depends on the multiplier μ, on the private spending flows c0 + I0 + NX, on the
interest-sensitivity parameter Ir, on the interest rate r, and on government purchases G


For this problem, assume a value of the Keynesian multiplier of μ = 2, and with Ir, the sensitivity of investment spending I to the interest rate r, such that Ir = $0.15T. And let’s use the Greek letter Δ—capital delta—as a shorthand symbol for changes from the previous equilibrium situation.


The Federal Reserve controls the short-term safe interest rate on government securities—it can nail that value to whatever it wants by buying and selling bonds for cash. We call this interest rate i. But the interest rate that matters for determining investment spending is the long-term real risky interest rate at which banks lend to companies. We call this interest rate r.


a) Suppose that the interest rate r that matters for investment spending falls by 1.5%-pts:
Δr = -1.5
By how much would you expect investment spending to fall given the parameter values of our model? How large is ΔI?

b) Continue your analysis from (a): given the parameter values of our model and the boosting of investment spending you calculated in (a), by how much would you expect GDP Y to grow?


c) Annual real GDP in the mid-2000s was about $15T. How large is this boost to GDP ΔY you calculated in (b) as a percentage of the then-level of real GDP?


d) On average, a 1% extra boost to GDP is associated with a 1.5% extra decrease in the unemployment rate. By how much extra would you expect the unemployment rate to fall as a
result of the boost to GDP you calculated in (b) and (c)?


e) Suppose that with the interest rate decline the unemployment rate falls from 6% to 4.5%. What would the unemployment rate have been without this interest-rate decline?

f) Suppose that real GDP had been lower for each of three years by the amount you calculated in (b). How much poorer would Americans have been in terms of reduced income over those three years had the interest rate r not fallen?


g) In an America with about 135 million workers, how much is this lost income per worker?

ECON 3050

Q24. The coefficient of determination (r2) is calculated as 0.49, then the correlation coefficient:

Cannot be determined without the data

Should be - 0.70 or 0.70

Should be 0.

Neither of the above

Q25. A regression line is used for all of the following except one. Which one is not a valid use of a regression line?

To estimate the average value of Y at a specified value of X.

To predict the value of Y for an individual, given that individual's X-value.

To estimate the change in Y for a one-unit change in X.

To determine if a change in X causes a change in Y.

Q26. Which choice is not an appropriate description of Yˆ in a regression equation?

Estimated response

Predicted response

Estimated average response

Observed response

Q27. Which of the following is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables?

Compute a regression line from a sample and see if the sample slope is 0.

Compute the correlation coefficient and see if it is greater than 0.5 or less than −0.5.

Conduct a test of the null hypothesis that the population slope is 0.

Conduct a test of the null hypothesis that the population intercept is 0.

Q28. There is no relationship between variables unless the data points lie in a straight line.

True

False

Q29. The sample regression analysis

Is the same as the population regression line

Is used to estimate the population regression line

Shows the true relation between dependent and independent variables

None of the above.

Q30. In regression, a dependent variable is sometimes called a predictor variable.

True

False

Q31. In a linear regression equation of the form y = a + bx, the intercept shows

The amount that y changes when x changes by one unit

The amount that x changes when y changes by one unit

The value of y when x is zero

The value of x when y is zero.

Q32. In a linear regression equation of y = a + bx, the slope b shows

Y / b

X / b

Y / X

X / Y

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