1.If the standard error of the estimate for a regression model fitted to a large

Question

1.If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within:(Please explain)

a. -3.50 and +3.50

b. -1.75 and +1.75

c. -0.95 and +0.95

d. -0.68 and +0.68

2. If the correlation coefficient (r)=1.0, then all the data points must fall exactly on a: (Please explain)

a. A straight line with a slope that equals 1.0

b. A straight line with a negative slope

c. A straight line with a positive slope

d. A horizontal line with a zero slope

Explanation / Answer

1. In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviation

So for 95% value will lie within +/-2 sd

So here 95% of the residuals would lie within +/-1.75*2=+/-3.50

Hence answer is a.

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