7. We want to see if there is a connection between the size of crops (in kg per unit area), rainfall (dry or wet year, indicated by 0 and 1, respectively), and mean temperature (in degrees celcius). We have observations from 30 different years, and the data are plotted in Figure 3. Some model output obtained in R. is shown below. Call: in (formula - Crop Temperature) Coefficients: Call: In(formula Crop Temperature + Rainfall) Estimate Std. Error t value Pr (>|t|) (Intercept) 32.5970 5.8178 5.603 5.350-06 Temperature -0.6075 0.2407 -2.524 0.0176 Coefficients: Estimate Std. Error t value Pr(>|t|) 11.1978 2.517 0.0181 0.4484 -0.966 0.3426 1.6862 0.464 0.6467 Figure 2: R output from two models fitted to the data of question 7. (a) Comment on the plots shown in Figure 3, specifically focusing on the correlation between the three variables. [3 marks] [4 marks] in terms of [3 marks] (Intercept) 28.1855 Temperature -0.4332 Rainfall 0.7817 (b) Give the mathematical expressions for both fitted models shown above. (c) Interpret the model that includes Rainfall and Temperature as covariates the estimated effect of the covariates on expected Crops. (d) Test the null hypothesis that the effect of Temperature on Crops is not significant at the 5% significance level (i) when Temperature is the only explanatory variable in the model. (ii) after accounting for the effect of Rainfall. Comment on your findings by referring to your answer in part (a). [2 marks] [2 marks] [2 marks] (e) It has been suggested that the interaction between Rainfall and Temperature should also be considered in the model. Give the mathematical expression for the model including this interaction term and explain what a significant interaction between the two covariates suggests about their effect on the response, using an example to demonstrate your point. [4 marks]
7. We want to see if there is a connection between the size of crops (in kg per unit area), rainfall (dry or wet year, indicated by 0 and 1, respectively), and mean temperature (in degrees celcius). We have observations from 30 different years, and the data are plotted in Figure 3. Some model output obtained in R. is shown below. Call: in (formula - Crop Temperature) Coefficients: Call: In(formula Crop Temperature + Rainfall) Estimate Std. Error t value Pr (>|t|) (Intercept) 32.5970 5.8178 5.603 5.350-06 Temperature -0.6075 0.2407 -2.524 0.0176 Coefficients: Estimate Std. Error t value Pr(>|t|) 11.1978 2.517 0.0181 0.4484 -0.966 0.3426 1.6862 0.464 0.6467 Figure 2: R output from two models fitted to the data of question 7. (a) Comment on the plots shown in Figure 3, specifically focusing on the correlation between the three variables. [3 marks] [4 marks] in terms of [3 marks] (Intercept) 28.1855 Temperature -0.4332 Rainfall 0.7817 (b) Give the mathematical expressions for both fitted models shown above. (c) Interpret the model that includes Rainfall and Temperature as covariates the estimated effect of the covariates on expected Crops. (d) Test the null hypothesis that the effect of Temperature on Crops is not significant at the 5% significance level (i) when Temperature is the only explanatory variable in the model. (ii) after accounting for the effect of Rainfall. Comment on your findings by referring to your answer in part (a). [2 marks] [2 marks] [2 marks] (e) It has been suggested that the interaction between Rainfall and Temperature should also be considered in the model. Give the mathematical expression for the model including this interaction term and explain what a significant interaction between the two covariates suggests about their effect on the response, using an example to demonstrate your point. [4 marks]
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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This question is part of a passed paper for an exam I am studying for. It is not marked coursework and I already have the answers, but I'd like to see an explained solution. Please see image attached for the question.
![7. We want to see if there is a connection between the size of crops (in kg per unit area),
rainfall (dry or wet year, indicated by 0 and 1, respectively), and mean temperature (in
degrees celcius). We have observations from 30 different years, and the data are plotted in
Figure 3. Some model output obtained in R. is shown below.
Call:
In (formula = Crop Temperature)
Coefficients:
Estimate Std. Error t value Pr (>|t|)
(Intercept) 32.5970 5.8178 5.603 5.350-06
Temperature -0.6075 0.2407 -2.524 0.0176
Call:
In(formula = Crop Temperature + Rainfall)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
11.1978 2.517 0.0181
0.4484 -0.966 0.3426
1.6862 0.464 0.6467
(Intercept) 28.1855
Temperature -0.4332
Rainfall 0.7817
Figure 2: R output from two models fitted to the data of question 7.
(a) Comment on the plots shown in Figure 3, specifically focusing on the correlation
between the three variables.
[3 marks]
[4 marks]
(b) Give the mathematical expressions for both fitted models shown above.
(c) Interpret the model that includes Rainfall and Temperature as covariates
the estimated effect of the covariates on expected Crops.
in terms of
[3 marks]
(d) Test the null hypothesis that the effect of Temperature on Crops is not significant at
the 5% significance level
(i) when Temperature is the only explanatory variable in the model.
(ii) after accounting for the effect of Rainfall.
Comment on your findings by referring to your answer in part (a).
[2 marks]
[2 marks]
[2 marks]
(e) It has been suggested that the interaction between Rainfall and Temperature should
also be considered in the model. Give the mathematical expression for the model including
this interaction term and explain what a significant interaction between the two covariates
suggests about their effect on the response, using an example to demonstrate your point.
[4 marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff88c1bed-f8e1-4a31-8ed9-f4891a69250d%2Fc52778e3-af07-4b97-9e85-5c709b977085%2Fv8gssos_processed.png&w=3840&q=75)
Transcribed Image Text:7. We want to see if there is a connection between the size of crops (in kg per unit area),
rainfall (dry or wet year, indicated by 0 and 1, respectively), and mean temperature (in
degrees celcius). We have observations from 30 different years, and the data are plotted in
Figure 3. Some model output obtained in R. is shown below.
Call:
In (formula = Crop Temperature)
Coefficients:
Estimate Std. Error t value Pr (>|t|)
(Intercept) 32.5970 5.8178 5.603 5.350-06
Temperature -0.6075 0.2407 -2.524 0.0176
Call:
In(formula = Crop Temperature + Rainfall)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
11.1978 2.517 0.0181
0.4484 -0.966 0.3426
1.6862 0.464 0.6467
(Intercept) 28.1855
Temperature -0.4332
Rainfall 0.7817
Figure 2: R output from two models fitted to the data of question 7.
(a) Comment on the plots shown in Figure 3, specifically focusing on the correlation
between the three variables.
[3 marks]
[4 marks]
(b) Give the mathematical expressions for both fitted models shown above.
(c) Interpret the model that includes Rainfall and Temperature as covariates
the estimated effect of the covariates on expected Crops.
in terms of
[3 marks]
(d) Test the null hypothesis that the effect of Temperature on Crops is not significant at
the 5% significance level
(i) when Temperature is the only explanatory variable in the model.
(ii) after accounting for the effect of Rainfall.
Comment on your findings by referring to your answer in part (a).
[2 marks]
[2 marks]
[2 marks]
(e) It has been suggested that the interaction between Rainfall and Temperature should
also be considered in the model. Give the mathematical expression for the model including
this interaction term and explain what a significant interaction between the two covariates
suggests about their effect on the response, using an example to demonstrate your point.
[4 marks]
Transcribed Image Text:Figure 3
Rainfall
20 22
Temperature
24
20
07
30
Rainfall
23
Temperature
24
25
26
27
10
10
15
15
Crop
Crop
20
25
25
9
MAST5001/2022
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