ECON 2P91 Lecture Notes - Lecture 9: Simple Linear Regression, Linear Regression, Null Hypothesis

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yellowhamster106

19 Jan 2017

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In week 4, we focused on a linear regression with one regressor, which is often referred to as a simple linear regression model. Specification of a linear regression with one regressor: This regression is specified as follows: y i=1,2, ,n. The above model assumes direction of causality is from x (the regressor) to y (the regressand). The model is referred to as a regression of y (the regressand) on x (the regressor). The model also defines the population regression line (because it applies to the population), in which case. 1 are the parameters of the population regression line. Recall that a parameter is a numerical quantity which is computed for the entire population and the value of the parameter is always fixed, be it known or unknown. 0 is the intercept parameter (i. e. the value of the dependent variable y when the independent variable x is equal to zero).

Related Questions

1. Novo Nordisk A/S, a Danish firm, sells insulin and other drugs worldwide. Activella, an estrogen and progestin hormone replacement therapy sold by Novo-Nordisk, is examined using 33 quarters of data

Y = -204+.34X1-.17X2

(17.0) (-1.71)

Where Y is quarterly sales of Activella, X1 is the Novo's advertising of the hormone therapy, and X2 is the advertising of a similar product by Eli Lilly and Company, Novo-Nordisk's chief competitor. The parentheses contain t-values. Addition information is: Durbin-Watson = 1.9 and R2= .89. According to t distribution table , t .05,31=1,6955

Using the data for Novo-Nordisk, which is correct?

A. Both X1 and X2 are statistically significant.

B. Neither X1 nor X2 are statistically significant.

C. X1 is statistically significant but X2 is not statistically significant.

D. X1 is not statistically significant but X2 is statistically significant.

E. The Durbin-Watson statistic shows significant problems with autocorrelation.

2. Which is NOT true about the coefficient of determination?

A. As you add more variables, the R-square generally rises.

B. As you add more variables, the adjusted R-square can fall.

C. If the R-square is above 50%, the regression is considered significant.

D. The R-square gives the per cent of the variation in the dependant variable that is explained by the independent variables.

E. The higher is the R-square, the better is the fit.

3. Table: Sherwin-Williams Company new Data

Observations Sales Promotional Expenditures Selling Price Disposable Income

I y A P M

1 160 100 15 19

2 200 160 14 17.5

3 140 50 16.5 14

4 190 190 14.5 20

5 130 90 17 15.5

6 160 70 16 14.5

7 200 140 15 21.5

8 150 110 18 18

9 210 200 12 18.5

10 190 100 15.5 20

Total 1750 1250 151 179.5

Mean 175 125 15.1 17.95

A. What is the regression equation for paint sales using a multiple linear regression model?

B. If A=180, P=$14, and M= 20, what is an approximate 95 per cent prediction interval for paint sales?

harlequinsardine5

Need assistance with these problems!

1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X₁ + X₂ + X₃ + X₄
Subject to: X₁ + X₄%u2265 12 (shift 1)
X₁ + X₂%u2265 15 (shift 2)
X₂ + X₃%u2265 16 (shift 3)
X₃ + X₄%u2265 14 (shift 4)
all variables %u2265 0

Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3) 12
13
0
none of the above

2. When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and: (Points : 3)

finding the profit at every corner point of the feasible region to see which one gives the highest value.
moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
locating the point that is highest on the graph.
none of the above.
all of the above.

3. Multiple optimal solutions can occur when the objective function is __________ a constraint line. (Points : 3)

unequal to
equal to
linear to
parallel to

4. When applying linear programming to diet problems, the objective function is usually designed to: (Points : 3)

maximize profits from blends of nutrients.
maximize ingredient blends.
minimize production losses.
maximize the number of products to be produced.
minimize the costs of nutrient blends.

5. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: (Points : 3)

same product mix, different total profit.
different product mix, same total profit as before.
same product mix, same total profit.
different product mix, different total profit.

6. The corner point solution method: (Points : 3)

will yield different results from the isoprofit line solution method.
requires that the profit from all corners of the feasible region be compared.
will provide one, and only one, optimum.
requires that all corners created by all constraints be compared.
will not provide a solution at an intersection or corner where a non-negativity constraint is involved.

7. Consider the following linear programming problem.
Maximize 4X + 10Y
Subject to: 3X + 4Y %u2264 480 and 4X + 2Y %u2264 3 360
all variables %u2265 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).

What is the maximum possible value for the objective function? (Points : 3)

1032
1200
360
none of the above

8. When using Excel's Solver to input and solve a linear programming problem, it is essential that one perform an additional task before submitting the formulation. That important additional function is: (Points : 3)

guessing the values of the variables.
putting in a value for the objective function.
choosing the options for assuming both a linear model and non-negative variables.
resetting the parameters.
none of the above.

9. Consider the following linear programming problem.
Maximize 5X + 6Y
Subject to: 4X + 2Y %u2264 420 and 1X + 2Y %u2264 120
all variables %u2265 0

Which of the following points (X,Y) is not feasible? (Points : 3)

(50,40)
(20,50)
(60,30)
none of the above

10. ____________ is used to analyze changes in model parameters. (Points : 3)

Optimal solution
Feasible solution
Sensitivity analysis
None of the above

1. You are given only three quarterly seasonal indices and quarterly seasonally adjusted data for the entire year. What is the raw data value for Q4? Raw data is not adjusted for seasonality.

Quarter Seasonal Index Seasonally Adjusted Data

Q1 .80 295

Q2 .85 299

Q3 1.15 270

Q4 --- 271

2. One model of exponential smoothing will provide almost the same forecast as a liner trend method. What are linear trend intercept and slope counterparts for exponential smoothing?

A. Alpha and Delta

B. Delta and Gamma

C. Alpha and Gamma

D. Standard Deviation and Mean

3. When performing correlation analysis what is the null hypothesis? What measure in Minitab is used to test it and to be 95% confident in the significance of correlation coefficient.

A. Ho: r = .05 p < .5

B. Ho: r = 0 p >.05

C. Ho: r ? 0 p?.05

D. Ho: r = 0 p?.05

In decomposition what does the cycle factor (CF) of .80 represent for a monthly forecast estimate of a Y variable?

A. The estimated value is 80% of the average monthly seasonal estimate.
B. The estimate is .80 of the forecasted Y trend value.
C. The estimated value is .80 of the historical average CMA values.
D. The estimated value has 20% more variation than the average historical Y data values.

5. A Wendy's franchise owner notes that the sales per store has fallen below the stated national Wendy's outlet average of $1,368,000. He asserts a change has occurred that reduced the fast food eating habits of Americans. What is his hypothesis (H1) and what type of test for significance must be applied?

A. H1: u ? $1,368,000 A one-tailed t-test to the left.
B. H1: u = $1,368,000 A two-tailed t-test.
C. H1: u < $1,368,000 A one-tailed t-test to the left.
D. H1: p < $1,368,000 A one-tailed test to the right

6. As the sample size from a population increases, for a given level of significance what happens to the null hypothesis rejection region and size of the t-table value?

A. The rejection region and the t-table value generally gets smaller for sample size below 31.
B. The rejection region gets larger and the t-table value generally gets smaller for sample sizes below 31.
C. The rejection region remains unchanged while the t-table value gets smaller for all sample sizes.
D. The zero mean hypothesis region gets larger and the t-table value gets larger as well for sample sizes below 31.

7. You obtained autocorrelation LBQ value of 18.58 for the 12^th lag from a data sample. Are the data significantly correlated at the lag examined or not? You want to be 95% confident in your answer.

A. Yes. The data are significantly correlated through the 12th lag.
B. No. The data are not significantly correlated through the 12^th lag.

C. No. Only the 12 lag period is not correlated.

D. You cannot tell since the number of sample observations is not provided.

E. The p-value is above .05 so the data is correlated.

8. Sometimes forecasters get lazy or forgetful and do not check the significance of XY data correlations and use the X variable to forecast Y. What is the result of this?

A. Type 2 error
B. Autocorrelation error
C. Type 3 error
D. Type 1 error

9. Do error measures indicate the statistical significance of forecast model variables?

A. Yes. They move in the same direction as statistical significance.
B. Yes. As error measures decrease the variable significance increases.
C. No They indicate only the magnitude of estimate error.
D. No. They indicate only the statistical significance of a forecast or fitted values.

10. In exponential smoothing what is the weight of the alpha coefficient for a time series data observation from the 3^rd previous period if the original alpha value is set at .8?

A. The weight cannot be calculated since the data observation is not given.
B. The weight is zero since the alpha value is set relatively high.
C. .548
D. .0064

11.Given the data series below for variables Y (Monthly Inventory Balance) and X (Monthly Sales) are they significantly correlated at the 95% confidence level and how can you tell?

Ending Inv. Bal. Y		Monthly Sales X
1544		5053
1913		5052
2028		7507
1178		2887
1554		3880
1910		4454
1208		3855
2467		8824
2101		5716

A. Yes. The correlation coefficient is .873 that is greater than .05.
B. Yes. The correlation p-value is .002 which is less than .05.
C. No. The correlation coefficient is above the p-value.
D.No. The correlation p-value is greater than the 95% confidence level.

12. You have forecast the sales for your company for the last 12 months and the forecast residuals are shown below. Are these residuals to be considered random?
Residuals

-24

-348

-892

-62

-378

-489

-342

490

578

198

A. Yes, since the residuals randomly vary in magnitude.
B. Yes since the residuals are positive and negative and vary in magnitude.
C. No, since the residuals are stationary and vary in magnitude.
D. No, since the residuals indicate positive slope.

13. Given the residuals in problem 12 above what is the RMSE for the forecast?

A. -101.0
B. 411.8
C. 169603
D. 220.1

14. Which form of exponential smoothing can result in a na

ECON 2P91 Lecture Notes - Lecture 9: Simple Linear Regression, Linear Regression, Null Hypothesis

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