Topic: Correlation and Regression. Using the F-distribution table to find the answers where necessary. D) , e) and f) need answers for these questions attached.
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D) , e) and f)
need answers for these questions attached.
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Given a generic data set (x,y) with a linear regression. How do you determine if the y(dependent) will be less/greater than a certain value at a decided value of x?The systolic blood pressure dataset (in the third sheet of the spreadsheet linked above) contains the systolic blood pressure and age of 30 randomly selected patients in a medical facility. What is the equation for the least square regression line where the independent or predictor variable is age and the dependent or response variable is systolic blood pressure? Y=__________ X + ______________ Patient 7 is 67 years old and has a systolic blood pressure of 170 mm Hg. What is the residual? __________ mm Hg Is the actual value above, below, or on the line? What is the interpretation of the residual? (difference in actual &predicated bp, difference in age, the amount of systolic changes)
- A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15a) What is dependent and independent variables? b) Fully write out the regression equation [1] c) Fill in the missing values ‘*’, ‘**’, ‘?’and ‘??’A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3% Analysis of VarianceSource DF SS MS F pRegression 3 1991.31…A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15 Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.
- A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15a) What is dependent and independent variables? [2]b) Fully write out the regression equation [1] c) Fill in the missing values ‘*’, ‘**’, ‘?’and ‘??’ [4] d) Hence test whether ? is significant. Give reasons for your answer. [4]…Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below. Say how you know from the output that there actually is a significant linear relationship between a male customer’s age at death and his father’s age at death. State the value of the coefficient of Father’s Age (Death) and interpret this value in the context of the problem at hand.State the value of the coefficient of determination in the model and interpret this value in the context of the situation.Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below Examine both the scatterplot and the correlation matrix provided above. Comment on the apparent relationship between the customer’s age at death and their father’s age at death in the plot. Explain how the information in the correlation matrix supports your conclusion
- The estimated regression equation for a model involving two independent variables and 10 observations follows.A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to2016:??=?+????+????+???IWhere FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processedusing MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-valueConstant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 **S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45a) What is dependent and independent variables?b) Fully write out the regression equationc) Fill in the missing values ‘*’, ‘**’, ‘?’and ‘??’d) Hence test whether ? is significant. Give reasons for your answer.e) Perform the F Test making…A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to2016:??=?+????+????+???IWhere FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processedusing MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-valueConstant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 **S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45 Hence test whether ? is significant. Give reasons for your answer.e) Perform the F Test making sure to state the null and alternative hypothesis.f) Given an interpretation of the term “R-sq” and comment on its value.