The following show the improvement (gain in reading speed) of 8 students in a sp
ID: 3052634 • Letter: T
Question
The following show the improvement (gain in reading speed) of 8 students in a speed-reading program, and the number of weeks they have been in the program: Number of weeks Speed gain ( words per minute) 86 118 49 193 164 232 73 109 2 4 (a) Make a scatter plot to verify that it is reasonable to assume that the regression of speed gain on the number of weeks is linear (b) Fit a straight line to the data using the method of least squares. (c) Test whether or not the slope ?-0 at a significance level of ?-001. (d) Give a point estimate of the mean speed gain when the number of weeks in the program is 12. (e) What additional danger is there when using your estimate in part (d)?Explanation / Answer
A) Scatter Plot shows it is reasonable to assume that regression of speed gain on the number of weeks is linear.
b) Model
y=a+b*x
y=3.341+24.932*x
Call:
lm(formula = y ~ x, data = y1)
Residuals:
Min 1Q Median 3Q Max
-10.0000 -6.3011 0.0341 6.4148 11.0682
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.341 7.430 0.45 0.669
x 24.932 1.345 18.53 1.59e-06 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 8.924 on 6 degrees of freedom
Multiple R-squared: 0.9828, Adjusted R-squared: 0.98
F-statistic: 343.5 on 1 and 6 DF, p-value: 1.592e-06
c) Test Whether B=0 at alpha=0.01
Which is less than <0.01 hence we reject null hypothesis of =0
d) Point estimate of mean spead when No of weeks =12
= 3.341+24.932*12
=302.525
e) Danger of using estimate in part d is that value of week=12 is outside range of week which used while building model.SO estimate might not be realistic.