Modelling Yield
Molineux Vineyards is interested in examining various factors relating to its annual yield of grapes in tons per acre over the period 1987-2016. Annual records of the following variables were available:
YIELD: Yield of grapes in the vineyards, in tons per acre.
RAIN: Centimetres of total rain fall during the rainy season.
DDAYS: Cumulative number of degree-days for the year. A degree-day is the number of degrees Fahrenheit above 50 degrees. Thus a day with 74 degree mean temperature would be a 24 degree-day. DDAYS is cumulated over the whole growing season.
TIME: Index of time, with TIME = 1 in 1987, 2 in 1988, 3 in 1989, etc.
FREEZE: Dummy variable coded 1 in those years in which there was a late killing frost.
NEW: Dummy variable that is coded 1 in those years in which a new management team was in place (i.e. 2007 to 2016).
Figure 1 (attached) present's descriptive statistics for the data and Figure 2 shows the correlation matrix of the variables. Figures 3 to 5 give various regression analysis output produced using Excel. Address the following questions, making sure to describe the modeling approach used:
(i) Explain in simple terms the meaning of the correlation coefficient between Rain and Yield in Figure 2.
(ii) Which variable(s) are significant at the 5% level in the regression model of Figure 3?
(iii) With reference to the model of Figure 3, what information is provided by the adjusted R2 and the standard error of estimate?
(iv) Does the residual plot in Figure 4 highlight any problems with the model in Figure 3? If yes, how could they be resolved?
(v) What does the model in Figure 5 suggest for the effectiveness of the new management?
(vi) One vineyard manager claims that the effect of a late killing frost on the yield of grapes in the vineyard is a reduction of 0.7 of a ton per acre. Using the output for the model in Figure 5, perform a test to examine whether there is evidence to reject this suggestion (using a 5% significance level).
(vii) What are the strengths and weaknesses of the model in Figure 5? Suggest ways in which it could be improved.
Attachment:- Assignment File.rar