a:
Calculate the coefficient.
a:
Explanation of Solution
The value of coefficient (b1) can be calculated as follows:
The value of coefficient is 0.123.
The intercept (b0) value can be calculated as follows:
The value of intercept is 281.7.
The general regression equation can be written as follows:
The terms
Thus, the sample regression equation can be written as follows:
The coefficient (Slope) indicates that increasing one unit of independent variable (fertilizer) leads to an increase in the dependent variable (yield) by 0.123.
b:
Testing the hypothesis.
b:
Explanation of Solution
Error sum of square (SSE) can be calculated as follows:
Error sum of square is 142.641.
The value of
The value of
Null hypothesis (H0) is
The t table value can be calculated as follows:
The t table value is 2.048.
The value of
The value of
Calculated t-value can be obtained as follows:
The t-value is 1.34. Since the calculated t-value is less than the t table value, the alternate hypothesis is not accepted.
c:
Coefficient of determination.
c:
Explanation of Solution
Coefficient of determination i
The coefficient for the determination is 0.0851. The R2 value indicates that 5.95% of the variation in the dependent variable is explained by the independent variable.
d:
Interpretation.
d:
Explanation of Solution
Since the R2 value is very low, it indicates that a weak relationship exists between he independent and dependent variables. Thus, the prediction would not be accurate.
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Chapter 16 Solutions
Statistics for Management and Economics (Book Only)
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