At a used dealership, let X be an independent variable representing the age in y

Question

At a used dealership, let X be an independent variable representing the age in years of a motorcycle and Y be the dependent variable representing the selling price of used motorcycle. The data is now given to you.

X = {5, 10, 12, 14, 15} Y = {500, 400, 300, 200, 100}

1.) Construct a 95% confidence interval for B1

2.) The lower bound is = _________ so only enter the second number of the interval here.

3.) The upper bound is = _________ so only enter the second number of the interval here.

4.) Does the data provide sufficient evidence to indicate that X contributes information to the prediction of Y?

5.) State the null and alternative hypothesis.

6.) What is the value of the test statistic?

7.) In conclusion, there is enough evidence to say that X contributes information to the prediction of Y. TRUE OR FALSE?

Explanation / Answer

(a) The 95% confidence interval for 1 is [-59.3146, -17.1185]

(b) Null hypothesis is Ho: 1 = 0

versus

Alternative hypothesis is Ha: 1 0

(c) The test statistic is t = -5.765

p- value = 0.0104

(d) Yes, there is enough evidence to say that X contributes information to the prediction of Y

Regression Analysis r² 0.917 n   5 r   -0.958 k   1 Std. Error   52.537 Dep. Var. y ANOVA table Source SS   df   MS F p-value Regression 91,719.7452 1   91,719.7452 33.23 .0104 Residual 8,280.2548 3   2,760.0849 Total 100,000.0000 4   Regression output confidence interval variables coefficients std. error    t (df=3) p-value 95% lower 95% upper std. coeff. Intercept 728.0255 0.000 x -38.2166 6.6295 -5.765 .0104 -59.3146 -17.1185 -0.958

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