(Updates with official prices) LONDON, Feb 5 (Reuters) - Copper prices rose on Friday, boosted by a weak dollar and hopes for better metals demand due to improved vaccine rollout and as the U.S. stimulus looked set to be approved. Three-month copper on the London Metal Exchange (LME) rose 1.9% to $7,970 a tonne by 1740 GMT. The metal, used in the power and construction industries, is on course for a weekly gain of about 1%. “Market sentiment has remained bullish but cautious this week,” said ING analyst Wenyu Yao. “In the short term there is not much of a directional signal for the metals markets as we head into the Chinese New Year and businesses wind down.” Global shares neared record highs as U.S. President Joe Biden’s drive to enact the $1.9 trillion coronavirus aid bill gained momentum after the U.S. Senate passed the budget plan. INVENTORIES: Global stocks of copper are at their lowest since 2008 despite the approaching Chinese New Year, when inventories usually build because of lower demand, broker Marex Spectron said in a note. Total inventories of copper in LME-registered warehouses are at 76,550 tonnes, less than half of October"s levels. MCUSTX-TOTAL SPREADS: The premium for LME cash copper over the three-month contract CMCU0-3 jumped to $14.50 a tonne, signalling tight nearby supply. The amount of cancelled inventory -- stock earmarked for delivery -- was high at 31% and fuelled concerns over tight LME copper. DOLLAR: The dollar retreated after the U.S. jobs report suggested that some traders may have over-egged a stronger American recovery from the coronavirus pandemic. A weaker dollar makes commodities it is priced in cheaper for holders of currencies. CHINA STOCKS: Metal held in warehouses monitored by the Shanghai Futures Exchange (ShFE) has increased ahead of the Chinese New Year. Zinc stocks ZN-STX-SGH jumped 34.9% week on week to 60,361 tonnes while ShFE tin inventories SSN-TOTAL-W rose 18.4% and ShFE aluminium stockpiles AL-STX-SGH increased by 10.2%. OTHER PRICES: LME aluminium gained 1.3% to $2,019 a tonne, zinc added 2% to $2,680, lead firmed by 0.5% to $2,055, tin added 1.1% to $23,085 and nickel was up 2.7% at $18,115.