A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft)and the quality of the resulting lawn.Eight similar plots of land are selected and each is planted with a particular density of seed.One month later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given below.Find a 95% confidence interval for the slope of the regression line.
Dependent variable is: Lawn Quality
R-squared = 36.0%
S = 9.073602 with 8 - 2 = 6 degrees of freedom
A)(-0.26,9.34)
B)(-1.51,10.58)
C)(14.77,51.53)
D)(27.10,39.18)
E)(-1.30,10.38)

Question

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft)and the quality of the resulting lawn.Eight similar plots of land are selected and each is planted with a particular density of seed.One month later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given below.Find a 95% confidence interval for the slope of the regression line.
Dependent variable is: Lawn Quality
R-squared = 36.0%
S = 9.073602 with 8 - 2 = 6 degrees of freedom 
A)(-0.26,9.34) 
B)(-1.51,10.58) 
C)(14.77,51.53) 
D)(27.10,39.18) 
E)(-1.30,10.38)

Quizplus · Accepted Answer

To find the confidence interval for the slope of the regression line, we need to use the t-distribution with degrees of freedom equal to n-2, where n is the number of data points (in this case, n=8). From the regression output, we can see that the slope estimate is 4.0351, and the standard error of the slope is 1.9489.

Using a 95% confidence level and the t-distribution with 6 degrees of freedom, we can find the t-value from the t-table or calculator to be 2.447.

The formula for the confidence interval is:

slope ± t-value * (standard error of slope)

Plugging in the values, we get:

4.0351 ± 2.447 * (1.9489)

Which simplifies to:

4.0351 ± 4.7678

Therefore, the 95% confidence interval for the slope of the regression line is (-0.7327, 8.8029), which corresponds to choice B.

A Grass Seed Company Conducts a Study to Determine the Relationship