辅导linear model、F-ratio留学生讲解、辅导R程序语言、R讲解
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Q2. How many observations have both pH greater than 5.99 pH units and K greater than 1.81 mg/litre ?
Q3. You are asked to use a linear model (e.g. using R's lm() function) to analyse whether Conductivity (units = micro S / cm ), in authority 25 , varies between four specific regions (labelled by the numbers: 1755, 1753, 1754, 1756 )
To fit this model you should:
1.Create a subset that contains data for only regions 1755, 1753, 1754, 1756 from authority 25
2.Transform the variable Conductivity using a power transformation with an exponent of 0.2
3.Fit a linear model with a response variable that is the power transformed Conductivity and an explanatory variable that is a single fixed factor which distinguishes between the four regions
From this analysis the estimated difference in the response variable between region 1753 and region 1755 is -0.23 (e.g. using the summary() function). What is the standard error for this estimate?
Q4. You are asked to use a linear model (e.g. using R's lm() function) to analyse whether Conductivity (units = micro S / cm ), in authority 7 , varies between four specific regions (labelled by the numbers: 293, 297, 295, 296 )
To fit this model you should:
1.Create a subset that contains data for only regions 293, 297, 295, 296 from authority 7
2.Transform the variable Conductivity using a power transformation with an exponent of 0.1
3.Fit a linear model with a response variable that is the power transformed Conductivity and an explanatory variable that is a single fixed factor which distinguishes between the four regions
The residual sum of squares from this analysis is 0.71 (e.g. using R's anova() function). What is the estimate for the F-ratio?
Q5. You are asked to use a linear model (e.g. using R's lm() function) to analyse whether Conductivity (units = micro S / cm ), in authority 25 , varies between four specific regions (labelled by the numbers: 1755, 1754, 1753, 1756 )
To fit this model you should:
1.Create a subset that contains data for only regions 1755, 1754, 1753, 1756 from authority 25
2.Transform the variable Conductivity using a power transformation with an exponent of 0.2
3.Fit a linear model with a response variable that is the power transformed Conductivity and an explanatory variable that is a single fixed factor which distinguishes between the four regions
Which of the following statements best describes the outcome of the linear model analysis and is suitable for inclusion in a scientific report?
For water samples from regions 1755, 1754, 1753, 1756 within water authority number 25, the average value of Conductivity is the same across the regions (F3, 320=1.2, p=0.32).
For water samples from regions 1755, 1754, 1753, 1756 within water authority number 25, the average value of Conductivity differs across the regions (p<0.05).
For water samples from regions 1755, 1754, 1753, 1756 within water authority number 25, the average value of Conductivity differs across the regions (F3, 320=53, p=0.32).
For water samples from regions 1755, 1754, 1753, 1756 within water authority number 25, the average value of Conductivity differs across the regions (F3, 320=1.2, p=0.32).
For water samples from regions 1755, 1754, 1753, 1756 within water authority number 25, the average value of Conductivity is the same across the regions (F3, 320=53, p=0.32).
Q6. For data from 'Area' C, what is the intercept of the best-fit regression line with 'Mg' (units=mg/litre) as the dependent (y-axis) variable and 'pH' (units=pH units) as the independent (x-axis) variable?
You should give your answer to 2 significant figures.
Q7. For data from 'Area' C, what is the standard error on the slope of the best-fit regression line with 'K' (units=mg/litre) as the dependent (y-axis) variable and 'NH4' (units=mg/kg) as the independent (x-axis) variable?
You should give your answer to 2 significant figures.
Q8. For data from 'Area' A, fit a linear model with 'K' (units=mg/litre) as the dependent (y-axis) variable and 'Mg' (units=mg/litre) as the independent (x-axis) variable. From the results of your model, which of the following statements is correct and suitable for a scientific report?
We find evidence of a linear relationship between K and Mg in area A (F1,34=120, p<0.005). The equation for the relationship between between K (units=mg/litre) and Mg (units=mg/litre) in area A is estimated to be K=0.8 + 1.3 Mg.
We find evidence of a linear relationship between K and Mg in area A (F1,10=26, p<0.005). The equation for the relationship between between K (units=mg/litre) and Mg (units=mg/litre) in area A is estimated to be K=-0.96 + 1.4 Mg.
We find evidence of a linear relationship between K and Mg in area A (F1,34=120, p<0.005). The equation for the relationship between between K (units=mg/litre) and Mg (units=mg/litre) in area A is estimated to be K=0.25 + 0.12 Mg.
We find no evidence of a relationship between K and Mg in area A (F1,10=26, p<0.005).
We find evidence of a linear relationship between K and Mg in area A (F1,10=26, p<0.005). The equation for the relationship between between K (units=mg/litre) and Mg (units=mg/litre) in area A is estimated to be K=0.55 + 0.27 Mg.
Q9. You are asked to test the null-hypothesis 'The relative frequencies of species?Sphagnum capillifolium?across the four regions H, O, Q, R are the same as those of species?Sphagnum fallax'.
Perform the appropriate chi-squared test for this null-hypothesis. What is the?expected?number of?Sphagnum capillifolium?in region H.
You should give your answer to 1 decimal place.
Q10. You are asked to test the null-hypothesis 'The relative frequencies of species?Sphagnum tenellum across the four regions G, J, O, R are the same as those of species Sphagnum capillifolium'
Perform the appropriate chi-squared test for this null-hypothesis. Which ONE of the following sentences, decsribing the result from this chi-squared test, would be the most appropriate for a scientific report?
The relative frequencies of?Sphagnum tenellum?across the four regions G, J, O, R differ from those of?Sphagnum capillifolium?(Chi-squared=21.6, df=25, p=0.66).
The relative frequencies of?Sphagnum tenellum?across the four regions G, J, O, R are the same as those of?Sphagnum capillifolium?(p=0.35).
The relative frequencies of?Sphagnum tenellum?across the four regions G, J, O, R are the same as those of?Sphagnum capillifolium?(Chi-squared=2.8, df=3, p=0.42).
The relative frequencies of?Sphagnum tenellum?across the four regions G, J, O, R are the same as those of?Sphagnum capillifolium?(Chi-squared=0.9, df=1, p=0.35).
The relative frequencies of?Sphagnum tenellum?across the four regions G, J, O, R differ from those of?Sphagnum capillifolium?(p=0.42).