Question

You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring.  

You collect data to, to help estimate Fawn Count for the upcoming Spring season.  You collect data on over the past 10 years.

x1 = Adult Deer Count

x2 = Annual Rain in Inches

x3 = Winter Severity

• Where Winter Severity Index:
  • 1 = Warm
  • 2 = Mild
  • 3 = Cold
  • 4 = Freeze
  • 5 = Severe

Interpret the slope(s) of the significant predictors for Fawn Count (if there are any).

Fawn count	Adult Count	Annual Rain in Inches	Winter Severity
2.9000001	9.19999981	13.19999981	2
2.4000001	8.69999981	11.5	3
2	7.19999981	10.80000019	4
2.29999995	8.5	12.30000019	2
3.20000005	9.6	12.60000038	3
1.89999998	6.80000019	10.60000038	5
3.4000001	9.69999981	14.10000038	1
2.09999991	7.9000001	11.19999981	3
2.99999995	8.7555559	12.34444319	4
3.49999995	10.6999998	14.20000038	1

• A. When you hold Annual Rain and Winter Severity constant, as Adult Count increases by 1, Fawn Count will increase by 0.3037.

  When you hold Adult Count and Winter Severity constant, as Annual Rain increases by 1 inch, Fawn Count will increase by 0.3978.

  When you hold Adult Count and Annual Rain constant, as Winter Severity increase by 1 and gets more harsh, Fawn Count will increase by 0.2493.

• B. When you hold Annual Rain and Winter Severity constant, as Adult Count increases by 1, Fawn Count will increase by 0.0852.

  When you hold Adult Count and Winter Severity constant, as Annual Rain increases by 1 inch, Fawn Count will increase by 0.0908.

  When you hold Adult Count and Annual Rain constant, as Winter Severity increase by 1 and gets more harsh, Fawn Count will increase by 0.0568.

• C. When you hold Annual Rain and Winter Severity constant, as Adult Count increases by 1, Fawn Count will increase by 0.9886.

  When you hold Adult Count and Winter Severity constant, as Annual Rain increases by 1 inch, Fawn Count will increase by 0.9774.

  When you hold Adult Count and Annual Rain constant, as Winter Severity increase by 1 and gets more harsh, Fawn Count will increase by 0.9661.

• D. There are no significant predictors

Answer 1

Supose we wish to test the significance of the regression model at 5% level. On regressing Fawn Count on the predictors Adult Count, Annual Rain in Inches and Winter Severity, the fitted regression model is obtained as:

We find that all the three predictors with p-values 0.012<0.05, 0.005 < 0.05 and 0.005 < 0.05 are significant at 5% level. The fitted regression model, using the estimated slope coefficients is expressed as:

Here, slope can be interpreted as the mean change in the response variable for a unit change in a predictor, other predictors in the model being constant.Here, changes observed woud be an 'increase', since, the slope for all the three predictors are positive.

Hence, the correct set of option would be:

A. When you hold Annual Rain and Winter Severity constant, as Adult Count increases by 1, Fawn Count will increase by 0.3037.

When you hold Adult Count and Winter Severity constant, as Annual Rain increases by 1 inch, Fawn Count will increase by 0.3978.

When you hold Adult Count and Annual Rain constant, as Winter Severity increase by 1 and gets more harsh, Fawn Count will increase by 0.2493.