[regression model confidence intervals] I can\'t seem to get correct answers for

Question

[regression model confidence intervals]

I can't seem to get correct answers for this question

Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. The accompanying data is on x = fluid flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 µm (mg/m3).

X: 87 | 177 | 185 | 354 | 363 | 442 | 968

Y: 0.44 | 0.60 | 0.50 | 0.66 | 0.62 | 0.69 | 0.91

(d) Estimate the true average change in mist associated with a 1 cm/sec increase in velocity, and do so in a way that conveys information about precision and reliability. (Use = 0.05. Give answers accurate to 6 decimal places.)

Explanation / Answer

From the given data
The regression equation is Y = 0.449 + 0.000495 X

The Estimate the true average change in mist associated with a 1 cm/sec increase in velocity is 0.000495

i.e. Estimate the true average change in mist = 0.000495 [the slope of the line]

The 95% confidence interval of the slope is (0.00033085,0.00066008)

where Zero is not contain in the interval, therefore, the slope of the regression equation is significant

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