If we fit a linear trend to 10 observations on time-series data that are growing exponentially,...

Question

Question

If we fit a linear trend to 10 observations on time-series data that are growing exponentially,...

If we fit a linear trend to 10 observations on time-series data that are growing exponentially, then it is most likely that:
1. the fitted trend will be too high at t = 1 and t = 10.
2. the fitted trend will be too low in the middle.
3. the forecasts (if extrapolated) will be too low.
4. the residuals will show a pattern like - - - + + + + - - -.

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Ans:

Option c is correct.

the forecasts (if extrapolated) will be too low.

As, for exponential distribution,larger values of t will give very smaller predicted values.

Add a comment

Answer 2

Similar Homework Help Questions

Please explain your answer Suppose that we use least-squares to fit a polynomial trend to this...

Please explain your answer Suppose that we use least-squares to fit a polynomial trend to this time series. Figure 4 displays the original time series plot along with the fitted values. Time Series and Polynomial Fit of the Trend 10 15 Time Figure 4 Which of the following characteristics is the model able to capture? Trend Seasonality Trend and seasonality Seasonality and heteroskedasticity
Please explain your answer Suppose that we use least-squares to fit a seasonal-means trend to this...

Please explain your answer Suppose that we use least-squares to fit a seasonal-means trend to this time series. Figure 3 displays the original time series plot along wtih the fitted values. Time Series and Seasonal-Means Fit 10 15 Time Figure 3 Which of the following characteristics is the model able to capture? Trend Seasonality ● Trend and seasonality Seasonality and heteroskedasticity
To make forecasts of a product’s price, we would like to check if a significant linear...

To make forecasts of a product’s price, we would like to check if a significant linear trend exists. Therefore, a linear regression model of the form price = b0 + b1*time has been formulated and fitted to the data with the output shown below. Which of the following would properly test and conclude if a significant trend exists in the time series? a. Test for Ho: b0 = 0. A significant linear trend exists. b. Test for Ho: b0 =...

Consider the following time series data. 15 13 10 12 a. Which of the following is a correct time series plot for this data? TimeSeries Value 14 12 10 TimePeriod (t) TimeSeries Value 14 12 10 TimePeri...

Consider the following time series data. 15 13 10 12 a. Which of the following is a correct time series plot for this data? TimeSeries Value 14 12 10 TimePeriod (t) TimeSeries Value 14 12 10 TimePeriod(t) TimeSeries Value 14 12 10 TimePeriod (t) 2 TimePeriod(t) select your answer- What type of pattern exists in the data? -select your answer b. Develop the linear trend equation for this time series (to 1 decimal). Tt = c. What is the forecast...
2 2. Suppose we are given data on n observations (i, Y),, and we have a...

2 2. Suppose we are given data on n observations (i, Y),, and we have a linear model, so that E(X)-A, + ßiri-Let呙-SXY /SXX and β') = F-β,2 be the least-square estimates given in lecture (a) Show that E(SXY)-ASXX and E (T)-A] + β,7. (b) Use (a) to show that E(角)-βι and E(A) = 3). In other words, these are unbiased estimators. (c) The fitted values Yt = Atari are used as estimates of E(A), and the residuals e.-Yi for...
QUESTION 9 Q9. For a time series with 17 time periods, the following linear trend expression...

QUESTION 9 Q9. For a time series with 17 time periods, the following linear trend expression was y't = 130.4 + 4.2t estimated: The forecast for time period 18 is _____________________ a. 197.6 b. 68.4 c. 206.0 d. 167.7 e. None of the above QUESTION 10 Q10: Which of the following inferences can be drawn from the scatter chart of residuals given below? a. The residuals have a varying variance. b. The model captures the relationship between the variables accurately. c....

2. Suppose we are given data on n observations (zi,Y), i = 1, , n, and...

2. Suppose we are given data on n observations (zi,Y), i = 1, , n, and we have a linear model, so that E(X) = β0+Axi. Let ßi-SXY/SXX and β0 = Y-Ax be the least-square estimates given in lecture. (a) Show that E(5xx) = ẢSXX and E(T) = β0+A2. (b) Use (a) to show that E(A) = and E(%) = A- In other words, these are unbiased estimators (c) The fitted values Y BotBr, are used as estimates of E(Y),...
Consider the following time series data 4 10 13 15 a. Which of the following is...

Consider the following time series data 4 10 13 15 a. Which of the following is a correct time series plot for this data? TimeSeries Value 14 12 10 4 2 TimePeriod(t) TimeSeries Value 14 12 10 4 2 TimePeriod(t) TimeSeries Value 14 7つ TimeSeries Value 14 12 10 8 TimePeriod(t) 3. TimeSeries Value 14 12 10 TimePeriod (t -Select your answer+ What type of pattern exists in the data? -Select your answer- b. Develop the linear trend equation for...
Consider the following time series data. t 1 2 3 4 5 Yt 6 12 9...

Consider the following time series data. t 1 2 3 4 5 Yt 6 12 9 14 16 a. Which of the following is a correct time series plot for this data? time series plot #1 time series plot #2 time series plot #3 1. 2. 3. What type of pattern exists in the data? linear trend curvilinear trend horizontal b. Develop the linear trend equation for this time series (to 1 decimal). Tt = ___ + ____t c. What...

2. Suppose we are given data on n observations (x,Y), i 1,... , n, and we...

2. Suppose we are given data on n observations (x,Y), i 1,... , n, and we have a linear model, = SXY/SXX and A,-ㄚ-Ax be the least-square estimates so that E(X) = β0 +ATp Let given in lecture. (a) Show that E(5xx)-A5xx and E(Y)-Ao +A2. (b) Use (a) to show that E(A)-A and E(A)-A. În other words, these are unbiased estimators (c) The fitted values Yi = ArtAz; are used as estimates of E(K), and the residuals ei = Y-...

If we fit a linear trend to 10 observations on time-series data that are growing exponentially,...

Homework Answers

Add Answer to:
If we fit a linear trend to 10 observations on time-series data that are growing exponentially,...

Post as a guest

Earn Coins

Please explain your answer Suppose that we use least-squares to fit a polynomial trend to this...

Please explain your answer Suppose that we use least-squares to fit a seasonal-means trend to this...

To make forecasts of a product’s price, we would like to check if a significant linear...

Consider the following time series data. 15 13 10 12 a. Which of the following is a correct time series plot for this data? TimeSeries Value 14 12 10 TimePeriod (t) TimeSeries Value 14 12 10 TimePeri...

2 2. Suppose we are given data on n observations (i, Y),, and we have a...

QUESTION 9 Q9. For a time series with 17 time periods, the following linear trend expression...

2. Suppose we are given data on n observations (zi,Y), i = 1, , n, and...

Consider the following time series data 4 10 13 15 a. Which of the following is...

Consider the following time series data. t 1 2 3 4 5 Yt 6 12 9...

2. Suppose we are given data on n observations (x,Y), i 1,... , n, and we...

If we fit a linear trend to 10 observations on time-series data that are growing exponentially,...

Homework Answers

Add Answer to: If we fit a linear trend to 10 observations on time-series data that are growing exponentially,...

Post as a guest

Earn Coins

Add Answer to:
If we fit a linear trend to 10 observations on time-series data that are growing exponentially,...