A series of laboratory experiments were carried out to investigate the relationship between the voltage level applied to

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A Series Of Laboratory Experiments Were Carried Out To Investigate The Relationship Between The Voltage Level Applied To 1 (119.88 KiB) Viewed 25 times

A series of laboratory experiments were carried out to investigate the relationship between the voltage level applied to an electronic component, and the lifetime (in weeks) of the component. In particular, voltages in the set {5, 6, 7, 8, 9, 10} were considered and, for each voltage, six components were tested until failure. Thus, the total sample size was n = 36 components. We define the following: . L = the lifetime of the component in weeks, .Y = In(L) the natural logarithm of the lifetime, and X = the voltage level. Furthermore, the following quantities have been calculated for you: ΣΥ, = 4.6 ΣΥ? = 177.1 ΣΧΥ, = -99.4 ΣΧ, = 270 ΣΧ2 = 2130 Lifetime versus Voltage In(Lifetime) versus Voltage In Lifetime i 0 5 6 9 10 5 6 9 10 8 X = Voltage 8 X = Voltage a) Show that the correlation between X and Y is -0.98, and comment on this value. Would you expect the magnitude of the correlation between X and L to be greater than or less than this? Make reference to the above scatterplots in your answer. (4 marks) b) Estimate the coefficients of the regression equation Y = Bo + B,X, and interpret the slope of this line. (5 marks) c) Comment on how well the regression model fits the data based on its coefficient of determination. (2 marks) d) Show that, from the equation in part (b), one can obtain the equation L = Lowt. Hence, or otherwise, predict the lifetime of the component when the voltage is 2V. Explain whether or not you believe the prediction to be accurate, and why. (4 marks) e) By computing a 95% confidence interval for B1, test the hypothesis that there is no relationship between log-lifetime and voltage level. Clearly state the hypotheses and provide your conclusion in both statistical and non-statistical language. (7 marks) f) Using the confidence interval from part (e), produce a confidence interval for w (where w appears in the model in part (d)). (3 marks)