Each student in a sample of lo was asked for the distance and the time required

Question

Each student in a sample of lo was asked for the distance and the time required to commute to college yesterday. The data collected are shown in the table. Distance 1 1 2 5 6 6 7 9 11 12 Time 5 10 5 15 10 15 15 15 25 25 Given an equation for the line of best fit of y = 4.22 + 1.63x, se^2 = 9.1440, sigma x = 60, and SS(x) = 138, make the following estimates. (a) Give a point estimate for the mean time required to commute 4 miles. (Give your answer correct to two decimal places.) (b) Give a 9O% confidence inter-val for the mean travel time required to commute 4 miles. (Give your answers correct to two decimal places.) (c) Give a 90% prediction interval for the travel time required for one person to commute the 4 miles. (Give your answers correct to two decimal places.) lower limit upper limit

Explanation / Answer

(b)

Lower limit = 8.72

Upper limit = 12.76

(c)

Lower limit = 4.76

Upper limit = 16.71

I have attached the corresponding excel sheet on the link given below.

https://drive.google.com/file/d/0ByUkX0Zrq3LBR0J3LUtsTUFLZTQ/view?usp=sharing

SUMMARY OUTPUT Regression Statistics Multiple R 0.913 R Square 0.834 Adj. R Square 0.813 Standard Error 3.024 Observations 10.000 ANOVA df SS MS F Significance F Regression 1.000 366.848 366.848 40.119 0.000 Residual 8.000 73.152 9.144 Total 9.000 440.000 Coefficients Standard Error t Stat P-value Lower 90.0% Upper 90.0% Intercept 4.217 1.817 2.322 0.049 0.839 7.595 Distance 1.630 0.257 6.334 0.000 1.152 2.109 The regression equation is Time-hat=4.217+1.630*Distance Mean = 6.00 St. Dev. = 3.92 Desired Pred. Level 90% alpha 10% Prediction at Point critical St. Error Margin of Lower Upper Interval Distance Prediction t-value of Prediction Error Bound Bound Length 4 10.74 1.86 3.21 5.97 4.76 16.71 11.95 Desired Conf. Level 90% alpha 10% Confidence at Point critical Standard Margin of Lower Upper Interval Distance Prediction t-value Error Error Bound Bound Length 4 10.74 1.86 1.09 2.02 8.72 12.76 4.04

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