2753 Trend Lines & Forecasting (No Seasonality)

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Based on the given data set, a trend line was created to represent the average age of first time mothers in Australia from 1989 to 2002. The trend line was then used to forecast the average age of first time mothers in 2003, and the result obtained was 30.2.

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The data provided shows that the average age of first-time mothers in Australia remained constant at 31.0 from 1989 to 2002. Therefore, it can be assumed that the trend line for this data would also be a horizontal line at 31.0. Based on this trend, it can be forecasted that the average age of first-time mothers in 2007 would also be 31.0.

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Based on the given information, the time series plot shows that there is seasonal variation in the data. Therefore, it is recommended to apply a trend line to the raw data in order to deseasonalize it and remove the seasonal variation.

Based on the information given, the time series plot shows that there is seasonal variation in the data. Therefore, applying a trend line to the raw data would not be appropriate. Instead, the data should be deseasonalized to remove the seasonal component before analyzing any trends.

The correct answer is "No, it appears to have cyclic variation." This is because the time series plot shows patterns that repeat at regular intervals, indicating the presence of cyclic variation. Therefore, applying a trend line to the raw data would not be appropriate as it would not capture the cyclic component of the data.

Based on the given time series plot, it can be observed that there is no clear pattern or trend in the data. The data points seem to fluctuate randomly without any consistent upward or downward movement. Therefore, applying a trend line to the raw data would not be necessary as it would not capture any meaningful trend.

For every month of coded time, the birth rate will decrease by 2. This means that as the coded time increases, the birth rate will decrease at a rate of 2 units per month.

The correct answer is Yes, it appears to have random variation only. Based on the information provided, the time series plot does not show any clear patterns or trends over time. Therefore, applying a trend line to the raw data would not be appropriate as it would not capture any meaningful information.

The gradient of the trend line represents the rate of change in the birth rate for each unit increase in the coded year. In this case, the gradient is 5, indicating that for every year of coded time, the birth rate will increase by 5.

The equation for the trend line is y=2173.74-12.95x. This equation represents a linear relationship between the dependent variable y and the independent variable x. The slope of the line is -12.95, indicating that for every unit increase in x, y decreases by 12.95 units. The y-intercept of the line is 2173.74, which represents the value of y when x is equal to zero. This equation suggests that there is a negative relationship between x and y, and it can be used to make predictions or estimate values of y based on different values of x.

The gradient in this context refers to the rate of change of the birth rate with respect to the coded time. The given equation shows that for every week of coded time, the birth rate will increase by 7. This means that as the coded time increases by one week, the birth rate will increase by 7 units.

The equation y=837.99+32.07x represents a linear trend line. It suggests that there is a positive relationship between the dependent variable (y) and the independent variable (x). For every unit increase in x, the value of y will increase by 32.07. The y-intercept is 837.99, indicating that when x is zero, the predicted value of y is 837.99. This equation is suitable for creating a trend line for the given data set.

The equation for the trend line is y=520.4+10.09x. This equation represents a linear relationship between the dependent variable y and the independent variable x. The constant term 520.4 represents the y-intercept, which is the value of y when x is 0. The coefficient 10.09 represents the slope of the line, indicating the rate of change in y for each unit increase in x. This equation suggests that as x increases, y increases at a rate of 10.09 units. Therefore, the given data set is suited to a trend line.

The given equation y=17.59-0.40x represents the equation for the trend line. It shows that the value of y is determined by the value of x, with a slope of -0.40. This means that for every increase of 1 in x, y will decrease by 0.40. The y-intercept is 17.59, indicating that when x is 0, y will be 17.59. This equation suggests that there is a negative linear relationship between x and y, where y decreases as x increases.

The gradient in this context refers to the coefficient or slope of the coded month variable in the trend line equation. The equation states that for every unit increase in coded month, the student attendance will decrease by 1.2. Therefore, the correct interpretation of the gradient is that for every month of coded time, student attendance will decrease by 1.2.

The equation for the trend line is y=12.47-0.26x. This equation represents a linear relationship between the variables x and y, where y decreases by 0.26 units for each unit increase in x. The y-intercept is 12.47, indicating that when x is 0, y is 12.47. This equation suggests that there is a negative correlation between x and y, and the trend line can be used to predict y values for different x values.

The equation given represents the trend line for the data set. It is in the form of y = mx + b, where m is the slope of the line (0.20) and b is the y-intercept (27.20). This equation can be used to predict the value of y for any given value of x in the data set.

The given answer "none" indicates that the data set (TS7E6) is not suited to a trend line. This means that there is no linear relationship or pattern that can be observed in the data, and therefore, it is not possible to create an equation for a trend line.

The gradient in this context refers to the coefficient of the coded month variable in the equation. Since the coefficient is negative (-1.3), it indicates that as the coded month increases by 1, the student attendance will decrease by 1.3. Therefore, for every month of coded time, student attendance will decrease by 1.3.

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The equation for the trend line is y=10.38+0.13x. This equation represents a linear relationship between the dependent variable y and the independent variable x. The coefficient 10.38 represents the y-intercept, which is the value of y when x is 0. The coefficient 0.13 represents the slope of the line, indicating the rate of change of y with respect to x. This equation suggests that as x increases by 1 unit, y will increase by 0.13 units. Therefore, the given equation is suitable for representing the trend in the data set.

The gradient of the trend line represents the rate of change of the dependent variable (student attendance) with respect to the independent variable (coded time). In this case, the gradient is -0.8, indicating that for every day of coded time, student attendance will decrease by 0.8.

The equation y=10.38+0.13x represents the trend line for the given data set TS7E8. The equation suggests that there is a linear relationship between the dependent variable y and the independent variable x. The slope of the line is 0.13, indicating that for each unit increase in x, y increases by 0.13 units. The y-intercept is 10.38, which represents the expected value of y when x is equal to zero. Therefore, this equation accurately represents the trend line for the given data set.

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The given answer is 702,000. This is because the question asks to predict the number of students enrolled in 2009 using the given data set. However, the data set provided only includes information from 1992 to 2001, so there is no data available for 2009. Therefore, the answer is that the prediction cannot be made based on the given data.

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The gradient of -0.5 indicates that for every week of coded time, the student attendance will decrease by 0.5. This means that as the coded time increases, the student attendance will gradually decrease at a rate of 0.5 per week.

The gradient in this context refers to the change in student attendance for each unit of coded time. Since the coefficient of the coded week is -0.8, it indicates that for every week of coded time, student attendance will decrease by 0.8. This means that as the coded time increases, the student attendance will gradually decrease.

Based on the information given, the correct answer is "Yes, it appears to have random variation only." This is because the time series plot does not show any clear patterns or trends. The data points appear to be scattered randomly without any noticeable upward or downward trend. Therefore, applying a trend line to the raw data would not be necessary as there is no evidence of any systematic or predictable variation in the data.

The gradient in this context refers to the coefficient of the coded week variable in the trend line equation. Since the coefficient is 4, it means that for every week of coded time, the birth rate will increase by 4.

The gradient in this context refers to the coefficient of the coded week variable (-1.2). A negative coefficient indicates a negative relationship between the coded week and the birth rate. Therefore, for every week of coded time, the birth rate will decrease by 1.2.

The correct answer is No, it appears to have cyclic variation. This is because the time series plot shows a pattern that repeats over a certain period of time, indicating the presence of cyclic variation.

The correct answer is "Yes, it appears to have random variation only." This can be inferred from the time series plot, which shows that there is no clear pattern or trend in the data. The data points seem to fluctuate randomly around a mean value, indicating that there is no systematic increase or decrease over time. Therefore, applying a trend line to the raw data would not be appropriate in this case.

The correct answer is No, it appears to have seasonal variation that needs to be deseasonalised. This is because the time series plot shows a repeating pattern or seasonality, indicating that there are regular fluctuations in the data over a specific time period. To analyze the underlying trend in the data, it is necessary to remove the seasonal component through deseasonalization techniques.

Based on the information provided, it can be inferred that the raw data does not exhibit a clear trend over time. Instead, it appears to have cyclic variation, meaning that there are repeated patterns or cycles in the data. Therefore, applying a trend line to the raw data would not be appropriate in this case.

Based on the given time series plot, it can be observed that there is no clear trend or pattern in the data. The data points seem to fluctuate randomly without any consistent upward or downward movement. Therefore, it is appropriate to apply a trend line to the raw data in order to identify any underlying trend or pattern.