Question 1

McMahon and Tate advertising company is interested in an appropriate mix of print, radio, and television ads for their new client. Darrin Stevens performs a multiple regression on the effects of dollars spent on each type of media on dollars of sales of product. Darrin uses data from the most recent advertising campaigns and develops the following equation: y = 254,215 + 6.79 × Print - 1.4 × Radio + 16.87 × Television
The r-squared statistic is 0.77 and all coefficients are significant. Which of the following statements is best?
A)At a minimum, the client will sell $254,215 worth of product after the new advertising campaign.
B)At a maximum, the client will sell $254,215 worth of product after the new advertising campaign.
C)This equation will be of no use in predicting the amount of sales based on advertising in these media.
D)The client should spend more money on television advertising than on radio advertising.

Accepted Answer

The coefficient for television advertising is the highest, indicating that it has the strongest positive effect on sales compared to the other two media. Additionally, the coefficient for radio advertising is negative, indicating that it has a negative effect on sales. Therefore, the client should focus on spending more money on television advertising and potentially decrease spending on radio advertising. Option A and B are incorrect because the $254,215 value is the constant term and does not represent a maximum or minimum. Option C is incorrect because the equation has a significant level of predictive power, as shown by the 0.77 R-squared value.

Question 2

A poultry farmer that dabbles in statistics is interested in exploring the relationship between two types of feed (layer pellets and scratch), water, and the output of his laying hens. For ten days he records the number of ounces of layer pellets and scratch the hens consume and the number of fluid ounces of water and tracks the number of eggs that are produced. After running a multiple regression model, he obtains the following report. What is the best interpretation of these statistics? $$\begin{array} { | l | c | c | c | c | } 
\hline & \text { Coefficients } & \text { Std Error } & t \text { Stat } & P \text {-value } \
\hline \text { Intercept } & 1.256 & 1.249 & 1.006 & 0.353 \
\hline \text { Scratch } & 0.185 & 0.032 & 5.714 & 0.001 \
\hline \text { Layer Pellets } & 0.295 & 0.026 & 11.539 & 0.000 \
\hline \text { Water } & 0.149 & 0.041 & 3.587 & 0.012 \
\hline
\end{array}$$
A)For every egg produced, about 0.185 ounces of scratch must be consumed.
B)The standard error for the model intercept is as large as the coefficient, thus the intercept is the most important predictor of egg production.
C)Layer pellets are not good predictors of egg production because the p-value is 0.
D)For every ounce of water consumed, the chickens produce 0.15 eggs, holding all other independent variables constant.

Accepted Answer

The coefficient for water is 0.149, meaning that for every ounce of water consumed, the number of eggs produced increases by 0.149, holding all other independent variables constant. This is the best interpretation of the statistics given. 
A is incorrect because it refers to the coefficient for scratch, not water. 
B is incorrect because the fact that the standard error for the intercept is as large as the coefficient does not imply that the intercept is the most important predictor. 
C is incorrect because layer pellets are actually good predictors of egg production based on the low p-value.

Question 3

Multiple regression was used to forecast success in college (GPA)based upon SAT score, high school GPA, and hours spent on-line. Use the regression output shown and comment on the overall fit of the model, the usefulness of each independent variable, and the value to an admissions department of using the model to make admission decisions. What is the model's forecast for an applicant having a high school GPA of 2.5 and an SAT score of 1000 that spends 20 hours a week on-line? What other variables do you feel would make good indicators of college GPA? $\begin{array}{l}
\text { Regression Statistics }\
\begin{array}{|l|c|c|c|c|c|}
\hline \text { Multiple R } & 0.718 & & & \
\hline \text { R Square } & 0.516 & & & & \
\hline \text { Adjusted R Square } & 0.273 & & & & \
\hline \text { Standard Error } & 0.339 & & & & \
\hline \text { Observations } & 10 & & & & \
\hline & & & & & \
\hline \text { ANOVA } & & & & & \
\hline & \text {df}  &\text {SS}  &\text { M S }&\text { F} &\text {Significance F} \
\hline \text { Regression } & 3 & 0.735 & 0.245 & 2.128 & 0.198 \
\hline \text { Residual } & 6 & 0.690 & 0.115 & & \
\hline \text { Total } & 9 & 1.425 & & & \
\hline & & & & & \
\hline &\text { Coefficients } & \text { Standard Error }  &\text { Stat } &\text { P-value } & \
\hline \text { Intercept } & 0.541 & 1.262 & 0.43 & 0.68 & \
\hline \text { HS GPA } & 0.423 & 0.307 & 1.38 & 0.22 & \
\hline \text { SAT } & 0.001 & 0.001 & 1.51 & 0.18 & \
\hline \text { On-Line } & 0.010 & 0.017 & 0.61 & 0.57 & \
\hline
\end{array}
\end{array}$

Accepted Answer

The answer of Multiple regression was used to forecast success...

Question 4

A poultry farmer that dabbles in statistics is interested in exploring the relationship between two types of feed (layer pellets and scratch), water, and the output of his laying hens. For ten days he records the number of ounces of layer pellets and scratch the hens consume and the number of fluid ounces of water and tracks the number of eggs that are produced. What is his regression equation based on the data? $$\begin{array} { | c | c | c | c | } 
\hline \text { Scratch } & \text { Layer Pellets } & \text { Water } & \text { Eggs } \
\hline 48 & 29 & 36 & 24 \
\hline 44 & 27 & 34 & 22 \
\hline 41 & 22 & 31 & 20 \
\hline 42 & 21 & 32 & 20 \
\hline 48 & 23 & 34 & 22 \
\hline 44 & 28 & 34 & 23 \
\hline 42 & 22 & 37 & 21 \
\hline 41 & 28 & 33 & 22 \
\hline 42 & 22 & 31 & 20 \
\hline 47 & 29 & 37 & 24 \
\hline
\end{array}$$
A)Eggs = 6.56 + .38Scratch + .17Pellets + .21Water
B)Eggs = 1.25 + .18Scratch + .29Pellets + .15Water
C)Eggs = 0.93 - .88Scratch + .37Pellets + .41Water
D)Eggs = 4.22 + .37Scratch + .67Pellets + .58Water

Accepted Answer

The correct regression equation is determined by using statistical software or methods to analyze the given data and find the coefficients that best fit the relationship between the variables (Scratch, Layer Pellets, Water) and the dependent variable (Eggs). Without performing the actual regression analysis here, it's not possible to directly calculate the correct equation. However, choice B is selected as the correct answer based on the context of the question, which implies a need for an explanation rather than the actual calculation process.

Question 5

Multiple regression is used when the forecaster believes that more than one independent variable should be used to predict the variable of interest.

Accepted Answer

Multiple regression is a statistical technique used to analyze the relationship between multiple independent variables and a dependent variable. It is used when the forecaster believes that more than one independent variable should be considered in predicting the dependent variable.

Question 6

Using the data in the table, first plot the data and comment on the appearance of the demand pattern. Then develop a forecast for periods 51-70 that fits the data.
 $\begin{array}{|c|c|c|c|c|c|c|c|}
\hline \text { Time } & \text { Output } & \text { Time } & \text { Output } & \text { Time } & \text { Output } & \text { Time } & \text { Output } \
\hline 1 & 12.5 & 14 & 16.4 & 27 & -19.2 & 40 & 11.3 \
\hline 2 & 14.8 & 15 & 11.7 & 28 & 10.6 & 41 & 11.1 \
\hline 3 & 15.3 & 16 & 11.1 & 29 & 16.8 & 42 & 52.5 \
\hline 4 & 15 & 17 & 11.9 & 30 & 22.5 & 43 & 11.3 \
\hline 5 & 11.5 & 18 & 11.3 & 31 & 15.5 & 44 & -19.3 \
\hline 6 & 11.6 & 19 & 13.7 & 32 & 11.7 & 45 & 12 \
\hline 7 & 12.8 & 20 & 16.3 & 33 & 11.9 & 46 & 15.5 \
\hline 8 & 51.9 & 21 & 13.1 & 34 & 13 & 47 & 20.5 \
\hline 9 & 11 & 22 & 10.8 & 35 & 11.9 & 48 & 16.5 \
\hline 10 & -19.7 & 23 & 10.3 & 36 & 13.5 & 49 & 12.5 \
\hline 11 & 11.9 & 24 & 11 & 37 & 16.5 & 50 & 10.5 \
\hline 12 & 17.8 & 25 & 51.4 & 38 & 14 & & \
\hline 13 & 20.3 & 26 & 11.6 & 39 & 11 & &\
\hline
\end{array}$

Accepted Answer

The answer of Using the data in the table, first...

Question 7

The ________ value for a regression or multiple regression model shows the percentage of variability in the dependent variable that is explained by the independent variable(s).

Accepted Answer

The answer of The ________ value for a regression or...

Question 8

A poultry farmer that dabbles in statistics is interested in exploring the relationship between two types of feed (layer pellets and scratch), water, and the output of his laying hens. For ten days he records the number of ounces of layer pellets and scratch the hens consume and the number of fluid ounces of water and tracks the number of eggs that are produced. After running a multiple regression model, he obtains the following report. What is the best interpretation of these statistics? Regression Statistics
$$\begin{array} { | l | c | } 
\hline \text { Multiple R } & 0.993633 \
\hline \text { R Square } & 0.987307 \
\hline \text { Adjusted R Square } & 0.98096 \
\hline \text { Standard Error } & 0.213764 \
\hline \text { Observations } & 10 \
\hline
\end{array}$$
A)The probability that the number of eggs is correctly predicted by the amount of scratch, layer pellets, and water consumed is 99.36%.
B)The prediction of the amount of eggs is 98.7% accurate based on the amount of scratch, layer pellets, and water consumed.
C)98.7% of the variability in egg production is explained by the amount of water, scratch, and layer pellets consumed.
D)The prediction of the amount of eggs is 99.36% accurate based on the amount of scratch, layer pellets, and water consumed.

Accepted Answer

The R Square value of 0.987307 indicates that 98.7% of the variability in egg production can be explained by the amount of water, scratch, and layer pellets consumed. This means that these three variables are highly predictive of the number of eggs produced. The other statistics, such as Multiple R and Standard Error, provide additional information about the strength and reliability of the relationship. However, neither A nor B accurately reflect the meaning of these statistics, and D is not quite correct as it refers to prediction accuracy rather than explaining variability.

Question 9

As yet another earthquake rattled her china cabinet, the data scientist decided to test whether hydraulic fracturing (where water is injected into the Earth)truly was predictive of the number of earthquakes in the region. What is the slope of the regression equation based on the data? $$\begin{array} { | c | c | } 
\hline \text { Injections } & \text { Earthquakes } \
\hline 137 & 682 \
\hline 331 & 833 \
\hline 360 & 905 \
\hline 442 & 1008 \
\hline 478 & 1482 \
\hline 529 & 1742 \
\hline
\end{array}$$
A)151.24
B)2.52
C)0.85
D)0.72

Accepted Answer

The slope ($m$) of the regression line can be calculated using the formula: $$m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$$ where $n$ is the number of observations, $x$ represents the injections, and $y$ represents the earthquakes. Plugging the given data into this formula gives a slope of approximately 2.52.

Question 10

A well-educated lumberjack decides to use linear regression to predict the demand for firewood based on the ambient temperature. He has collected data on firewood sales and temperature for the last several days and has performed some preliminary calculations as shown in the table. What is his regression equation based on the data? $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Temp } & \text { Ricks } & \text { Temp Squared } & \text { Temp *\# Ricks } \
\hline & 33 & 17 & 1089 & 561 \
\hline & 19 & 32 & 361 & 608 \
\hline & 34 & 20 & 1156 & 680 \
\hline & 34 & 18 & 1156 & 612 \
\hline & 20 & 33 & 400 & 660 \
\hline & 24 & 30 & 576 & 720 \
\hline & 17 & 34 & 289 & 578 \
\hline & 30 & 25 & 900 & 750 \
\hline & 38 & 16 & 1444 & 608 \
\hline & 23 & 29 & 529 & 667 \
\hline \text { Sums } & 272 & 254 & 7900 & 6444 \
\hline
\end{array}$$
A)Ricks = 50.6 - 0.93 × Temp
B)Temp = 53.3 - 1.0 × Ricks
C)Ricks = 0.93 - 50.6 × Temp
D)Temp = 1.0 - 53.3 × Ricks

Accepted Answer

The regression equation will be of the form Ricks = a + b × Temp. Using the information given in the table, we can calculate the values for a and b using the formulas:

b = [nΣ(Temp × #Ricks) - Σ(Temp)Σ(#Ricks)] / [nΣ(Temp^2) - (Σ(Temp))^2]
a = (Σ(#Ricks) - bΣ(Temp)) / n

where n is the number of data points. Plugging in the values from the table, we get:

b = [10(6444) - (272)(254)] / [10(7900) - (272)^2] ≈ -0.93
a = (254 - (-0.93)(272)) / 10 ≈ 50.6

So the regression equation is Ricks = 50.6 - 0.93 × Temp.

Question 11

As yet another earthquake rattled her china cabinet, the data scientist decided to test whether hydraulic fracturing (or fracking)truly was predictive of the number of earthquakes in the region. What proportion of the number of earthquakes is predicted by the number of water injections based on the available data? $$\begin{array} { | c | c | } 
\hline \text { Injections } & \text { Earthquakes } \
\hline 137 & 682 \
\hline 331 & 833 \
\hline 360 & 905 \
\hline 442 & 1008 \
\hline 478 & 1482 \
\hline 529 & 1742 \
\hline
\end{array}$$
A)0.96
B)0.89
C)0.85
D)0.72

Accepted Answer

The answer of As yet another earthquake rattled her china...

Question 12

A counseling service records the number of calls to their hotline for the last year. Plot the data and determine which forecasting technique would be best among a moving average, weighted moving average, exponential smoothing, and regression line.
 $$\begin{array} { | l | c | } 
\hline { \text { Month } } & \text { Demand } \
\hline \text { Tanuary } & 111 \
\hline \text { February } & 127 \
\hline \text { March } & 146 \
\hline \text { April } & 159 \
\hline \text { May } & 165 \
\hline \text { Tune } & 165 \
\hline \text { July } & 178 \
\hline \text { August } & 182 \
\hline \text { September } & 191 \
\hline \text { October } & 208 \
\hline \text { November } & 223 \
\hline \text { December } & 228 \
\hline
\end{array}$$

Accepted Answer

The answer of A counseling service records the number of...

Question 13

Demand was low two years ago but increased sharply last year thanks to an aggressive marketing campaign. A time series model that puts the greatest emphasis on the most recent period is probably the best choice to predict next year's demand.

Accepted Answer

The answer of Demand was low two years ago but...

Question 14

Which of these quantitative techniques can be a causal model?
A)linear regression
B)last period
C)exponential smoothing
D)weighted moving average

Accepted Answer

Linear regression can establish a causal relationship between two variables by identifying the effect of one variable on another. The other techniques mentioned are all forecasting techniques and do not establish causality.

Question 15

A poultry farmer that dabbles in statistics is interested in exploring the relationship between layer pellets and the output of his laying hens. For ten days he records the number of ounces of layer pellets and the number of eggs that are produced. What is his regression equation based on the data? $$\begin{array} { | c | c | } 
\hline \text { Layer Pellets } & \text { Eggs } \
\hline 29 & 24 \
\hline 27 & 22 \
\hline 22 & 20 \
\hline 21 & 20 \
\hline 23 & 22 \
\hline 28 & 23 \
\hline 22 & 21 \
\hline 28 & 22 \
\hline 22 & 20 \
\hline 29 & 24 \
\hline
\end{array}$$
A)Eggs = 11.3 + 0.42Pellets
B)Eggs = 1.25 + 0.29Pellets
C)Eggs = 10.9 + 0.23Pellets
D)Eggs = 4.22 + 0.67Pellets

Accepted Answer

To find the regression equation, we calculate the slope (m) and y-intercept (b) of the line that best fits the data points. Using the given data, the correct calculation results in the equation Eggs = 11.3 + 0.42Pellets, which matches choice A. This is determined by applying the formula for the slope and intercept from linear regression analysis, which involves summing the products of the differences from the means of the x (pellets) and y (eggs) values, and dividing by the sum of the squares of the differences from the mean of the x values for the slope. The intercept is found by subtracting the product of the slope and the mean of the x values from the mean of the y values.

Question 16

A poultry farmer that dabbles in statistics is interested in exploring the relationship between two types of feed (layer pellets and scratch), water, and the output of his laying hens. For ten days he records the number of ounces of layer pellets and scratch the hens consume and the number of fluid ounces of water and tracks the number of eggs that are produced. What is his regression equation based on the data?
 $$\begin{array} { | c | c | c | c | } 
\hline \text { Scratch } & \text { Layer Pellets } & \text { Water } & \text { Eggs } \
\hline 48 & 29 & 36 & 24 \
\hline 44 & 27 & 34 & 22 \
\hline 41 & 22 & 31 & 20 \
\hline 42 & 21 & 32 & 20 \
\hline 48 & 23 & 34 & 22 \
\hline 44 & 28 & 34 & 23 \
\hline 42 & 22 & 37 & 21 \
\hline 41 & 28 & 33 & 22 \
\hline 42 & 22 & 31 & 20 \
\hline 47 & 29 & 37 & 24 \
\hline
\end{array}$$

Accepted Answer

The answer of A poultry farmer that dabbles in statistics...

Question 17

The Pancake House did a brisk business on the weekend and the maître d' was always on the lookout for ways to improve the customer experience. He carefully tracked the number of customers that graced their establishment over the last four weekends. He was hopeful that he could forecast the number of customers that would come for the world's finest pancakes the next weekend.
 $$\begin{array} { | l | c | c | c | c | } 
\hline & \text { Weekend 1 } & \text { Weekend 2 } & \text { Weekend 3 } & \text { Weekend 4 } \
\hline \text { Friday } & 131 & 216 & 286 & 355 \
\hline \text { Saturday } & 225 & 311 & 408 & 490 \
\hline \text { Sunday } & 166 & 249 & 330 & 415 \
\hline
\end{array}$$ Using the data in the table, first plot the data and comment on the appearance of the demand pattern. Then develop a forecast for weekend #5 that fits the data.

Accepted Answer

The answer of The Pancake House did a brisk business...

Question 18

Heidi runs a multiple regression for the output of cheese curds by using the daily temperature and the consumption of sweet clover. The intercept term is 23, the slope coefficient for the daily temperature is 1.5 and the slope coefficient for the consumption of sweet clover is 0; both coefficients are statistically significant. Which of these conclusions is most appropriate?
A)Heidi should collect more data.
B)The most important term in Heidi's model is the intercept.
C)As the daily temperature rises, the intercept term probably decreases.
D)Heidi should drop the sweet clover term from her model.

Accepted Answer

Since the slope coefficient for the consumption of sweet clover is 0 and statistically significant, it means that this variable is not contributing to the output of cheese curds. Therefore, Heidi should drop the sweet clover term from her model.

Question 19

Using the data shown in the table, develop a regression line that can be used to predict the demand for time period number 20. What is the regression equation and what is your forecast for period 20?
 $$\begin{array} { | c | c | c | c | } 
\hline & \text { Period } & \text { Demand } & \text { Period } * \text { Demand } \
\hline & 1 & 16 & 16 \
\hline & 2 & 20 & 40 \
\hline & 3 & 24 & 72 \
\hline & 4 & 27 & 108 \
\hline & 5 & 29 & 145 \
\hline & 6 & 30 & 180 \
\hline & 7 & 32 & 224 \
\hline & 8 & 35 & 280 \
\hline & 9 & 36 & 324 \
\hline & 10 & 38 & 380 \
\hline \text { Sums } & 55 & 287 & 1769 \
\hline
\end{array}$$

Accepted Answer

The answer of Using the data shown in the table,...

Question 20

Models that predict values based upon some independent factor(s)other than time are ________ forecasting models.

Accepted Answer

The answer of Models that predict values based upon some...

Quiz 9: Forecasting

Multiple regression is used when the forecaster believes that more than one independent variable should be used to predict the variable of interest.

The ________ value for a regression or multiple regression model shows the percentage of variability in the dependent variable that is explained by the independent variable(s).

Demand was low two years ago but increased sharply last year thanks to an aggressive marketing campaign. A time series model that puts the greatest emphasis on the most recent period is probably the best choice to predict next year's demand.

Which of these quantitative techniques can be a causal model?

Models that predict values based upon some independent factor(s)other than time are ________ forecasting models.