The horsepower (Y, in bhp) of a motor car engine was measured at a chosen set of
ID: 3219450 • Letter: T
Question
The horsepower (Y, in bhp) of a motor car engine was measured at a chosen set of values of running speed (X, in rpm). The data are given below (the first row is the running speed in rpm and the second row is the horsepower in bhp):
The mean and sum of squares of the rpm are 3461.5385 rpm and 185040000.0000 rpm 22 respectively; the mean of the horsepower values is 164.3946 bhp and the sum of the products of the two variables is 8841094.0000 rpm bhp. A scatterplot displaying the data is shown below:
Compute the regression line for these data, and provide your estimates of the slope and intercept parameters. To calculate the slope and intercept please keep intermediate results to 6 decimal places (when you calculate the intercept do not round the value of the slope).
1100 1400 1700 2300 2700 3200 3500 4000 4300 4600 4900 5200 6100 rpm Horsepower (bhp) 47.03 54.82 80.55 119.8 123.43 140.23 167.95 198.2 205. 68 224. 86 2 35.4 24 51 290.64Explanation / Answer
The statistical software output for the given problem is:
Simple linear regression results:
Dependent Variable: Housepower (bhp)
Independent Variable: rpm
Housepower (bhp) = -6.2932167 + 0.049309818 rpm
Sample size: 13
R (correlation coefficient) = 0.99675535
R-sq = 0.99352122
Estimate of error standard deviation: 6.4954912
Parameter estimates:
Analysis of variance table for regression model:
Hence,
Intercept = -6.293217
Slope = 0.049310
Regression line:
y = -6.293217 + 0.049310 x
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -6.2932167 4.5295605 0 11 -1.3893658 0.1922 Slope 0.049309818 0.0012005906 0 11 41.071302 <0.0001Related Questions
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